Charlie Austin's sixth-minute penalty appeared to have Saints in control, with Hull offering little in the way of an attacking threat.
The hosts also lost starting strikers Abel Hernandez and Will Keane to first-half injuries to compound the frustration of their fans, but the mood inside the KCOM Stadium was transformed in the space of two second-half minutes.
First, Snodgrass - introduced from the bench for the stricken Keane - swept home his fourth league goal of the season from Sam Clucas' low cross before the Scotland international delivered an inviting free-kick that Michael Dawson headed past Fraser Forster.
Southampton pushed for an equaliser but David Marshall made a string of saves in the Hull goal before Clucas produced a remarkable goalline clearance from a corner in the final minute of added time.
The win - Hull's first in the league since 20 August - ends a six-game losing streak, although they remain inside the bottom three heading into the international break.
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The best that could be said for the early loss of Hull's strikers was that it gave an opportunity for Snodgrass to return earlier than expected after missing the past two matches with an ankle injury.
But his entrance from the bench following Keane's injury midway through the first half did not appear to be asking too much of the Tigers' top scorer - far from it.
Instantly the hosts appeared to have greater urgency with the 29-year-old on the pitch, having looked sluggish and uninspired for 26 minutes before his introduction.
The mood inside the stadium at kick-off was exactly what could be expected of a club bidding to avoid a seventh straight league defeat for the first time in 36 years.
That run of defeats - during which 20 goals had been shipped - allied to widespread unhappiness among fans over the Allam family's running of the club meant the KCOM Stadium had a threadbare look at kick-off, with an official attendance of just 17,768.
Empty seats dotted a ground that used to be filled to the rafters in the second and third tiers, and the dark mood of many home fans in attendance cannot have been lost on the players.
Yet Snodgrass' tireless running lifted not only the fans but his team-mates, and his well-taken 61st-minute goal followed moments later by a perfect assist for Dawson was just reward for his endeavour.
Southampton celebrated one of the most famous wins in their history by beating Inter Milan in the Europa League on Thursday, and a Hull side low on confidence did not look like dampening their mood in the opening exchanges.
Austin's early penalty - an easy decision for referee Graham Scott after Curtis Davies' clumsy challenge on Maya Yoshida - had the visitors in cruise control, with Hull allowing them time and space to pass the ball around, albeit with little cutting edge.
Virgil van Dijk's looping header off the bar early in the second half was as close as they came to doubling their lead, and that apparent lack of urgency came back to bite them when Hull struck their quick-fire double just after the hour mark.
That was the spark for Claude Puel's men to push forward with greater urgency, but in former Cardiff goalkeeper Marshall they found someone in determined mood after a miserable start to life between the sticks in East Yorkshire.
The Scotland international - whose elevation to number one ahead of Eldin Jakupovic coincided with Hull's slump in form - twice saved well from Austin as time ticked down, and also kept out a Yoshida effort.
Dawson then came to the rescue to heroically block from Austin, before Clucas produced a stunning goalline clearance deep in added time, the winger hacking the ball off the line, against Jay Rodriguez and somehow over the bar.
Hull City boss Mike Phelan, speaking to Match of the Day: "I'm really pleased for my players. We lost two players early in the game to what look like long injuries. The players are ecstatic. I thought we caused our own problems in the first half giving the penalty away and not getting the ball quick enough.
"The players were a credit. Our keeper David Marshall has had a hard time of late but he was magnificent. Robert Snodgrass had the most unbelievable swollen ankle at one point which disappeared overnight. He showed great character.
"Now that we have got three or four injuries, the international break has come at a good time for us. We will enjoy the next few days and start again."
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Southampton manager Claude Puel, speaking to Match of the Day: "We lacked concentration. We lost the rhythm of the game. It is important for the future that we learn from this situation.
"After a European game it is difficult to keep the same concentration. It is a good lesson for the future.
"We know all the teams are difficult to play and to play every three days is difficult. We have to learn this and keep the same concentration every game."
Following the international break, Hull return to action with a trip to bottom side Sunderland on Saturday, 19 November (15:00 GMT), while on the same day Southampton play host to leaders Liverpool, also at 15:00.
Match ends, Hull City 2, Southampton 1.
Second Half ends, Hull City 2, Southampton 1.
Delay over. They are ready to continue.
Delay in match Dieumerci Mbokani (Hull City) because of an injury.
Corner,  Southampton. Conceded by David Marshall.
Attempt saved. Maya Yoshida (Southampton) header from the right side of the six yard box is saved in the bottom right corner. Assisted by Sofiane Boufal with a cross.
Attempt blocked. Jay Rodriguez (Southampton) right footed shot from the centre of the box is blocked. Assisted by Sofiane Boufal.
Attempt missed. Robert Snodgrass (Hull City) right footed shot from outside the box is too high. Assisted by Sam Clucas following a set piece situation.
Oriol Romeu (Southampton) is shown the yellow card for a bad foul.
Foul by Oriol Romeu (Southampton).
Ryan Mason (Hull City) wins a free kick in the defensive half.
Attempt blocked. Charlie Austin (Southampton) right footed shot from the centre of the box is blocked.
Sofiane Boufal (Southampton) wins a free kick on the left wing.
Foul by Robert Snodgrass (Hull City).
Corner,  Southampton. Conceded by Tom Huddlestone.
Attempt missed. Virgil van Dijk (Southampton) header from the centre of the box is close, but misses to the right. Assisted by James Ward-Prowse with a cross following a corner.
Corner,  Southampton. Conceded by Sam Clucas.
Attempt saved. Charlie Austin (Southampton) right footed shot from the centre of the box is saved in the bottom right corner. Assisted by James Ward-Prowse.
Attempt missed. Oriol Romeu (Southampton) left footed shot from outside the box misses to the right. Assisted by Maya Yoshida.
Oriol Romeu (Southampton) wins a free kick in the defensive half.
Foul by Dieumerci Mbokani (Hull City).
Attempt missed. Tom Huddlestone (Hull City) right footed shot from outside the box is just a bit too high following a corner.
Corner,  Hull City. Conceded by Steven Davis.
Maya Yoshida (Southampton) is shown the yellow card for a bad foul.
Foul by Maya Yoshida (Southampton).
Dieumerci Mbokani (Hull City) wins a free kick in the defensive half.
Attempt missed. James Ward-Prowse (Southampton) right footed shot from long range on the left is just a bit too high from a direct free kick.
Sofiane Boufal (Southampton) wins a free kick on the left wing.
Foul by Robert Snodgrass (Hull City).
Ryan Bertrand (Southampton) wins a free kick in the defensive half.
Foul by Markus Henriksen (Hull City).
Hand ball by Tom Huddlestone (Hull City).
Substitution, Southampton. James Ward-Prowse replaces Jordy Clasie.
Substitution, Southampton. Jay Rodriguez replaces Nathan Redmond.
Attempt saved. Charlie Austin (Southampton) right footed shot from outside the box is saved in the bottom left corner. Assisted by Sofiane Boufal.
Substitution, Hull City. Tom Huddlestone replaces Harry Maguire.
Foul by Sofiane Boufal (Southampton).
Ryan Mason (Hull City) wins a free kick in the attacking half.
Ryan Bertrand (Southampton) is shown the yellow card.
Corner,  Southampton. Conceded by Curtis Davies.
Robert Snodgrass inspired Hull City to victory against Southampton as Mike Phelan earned his first three points since being appointed permanent head coach.