The midfielder curled in from 20 yards following Ben Mee's foul on Tom Huddlestone.
Steven Defour had put Burnley in front when he picked the ball up in his own half, ran at goal and beat Eldin Jakupovic with a 30-yard shot.
Hull's David Meyler grazed a post at 0-0 and team-mate Curtis Davies almost equalised when heading against the bar.
The result means Hull, under the stewardship of caretaker manager Mike Phelan, drop a place to sixth in the table, while Burnley are 15th.
Snodgrass, who scored a hat-trick for Scotland in the World Cup qualifying win over Malta last Sunday, was at the heart of most of Hull's good work.
The 29-year-old made the slide rule pass in the first half which set up Meyler for the shot across goal which brushed a post.
Snodgrass also had a well-struck shot palmed over by Burnley keeper Tom Heaton before delivering the cross from which Davies' header hit the woodwork as Hull pressed for an equaliser.
He said of his free-kick: "Shaun Maloney came over and asked if I fancied it, and I said 'yes'."
Snodgrass, who spent 16 months out after dislocating a kneecap on his Premier League debut for Hull in August 2014, also scored Hull's winner in their opening game of the season against Leicester.
The two goals and late drama in the game were in contrast to the match as a whole between two sides promoted from the Championship last season.
Burnley boss Sean Dyche admitted his side were initially "edgy" after a 3-0 defeat by Chelsea in their previous league game.
While Hull had more possession, both sides lacked a cutting edge, but Defour changed that in brilliant fashion after 72 minutes with one of Burnley's two shots on target in the match.
The Belgium international was the club's £8m record signing from Anderlecht before the arrival of Jeff Hendrick for £10.5m on transfer deadline day.
Defour was replaced by debutant Hendrick almost immediately after his goal, which was his first for Burnley.
Burnley manager Sean Dyche: "I was pleased with performance. We started a bit edgy but built into the game.
"It's the way it goes. It is the reality of football. It was a game of few chances and cagey.
"He (Defour) was a cheap as chips - have you not seen what is happening in the Premier League? He is a fine player."
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Hull City caretaker boss Mike Phelan: "We suffered in the last minute in the last game (letting in a late goal against Manchester United).
"Credit to us as we kept going. The players did what we asked of them today."
On being appointed on a full-time basis: "I'm there in the dugout. I'm kicking every ball with the players and it is a joy."
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Burnley's next game takes them to Leicester, while Hull host Arsenal, with both games at 15:00 BST on Saturday, 17 September.
Match ends, Burnley 1, Hull City 1.
Second Half ends, Burnley 1, Hull City 1.
Goal!  Burnley 1, Hull City 1. Robert Snodgrass (Hull City) from a free kick with a left footed shot to the bottom right corner.
Tom Huddlestone (Hull City) wins a free kick in the attacking half.
Foul by Ben Mee (Burnley).
Corner,  Hull City. Conceded by George Boyd.
Attempt missed. Abel Hernández (Hull City) right footed shot from the centre of the box misses to the left.
Attempt missed. Ahmed Elmohamady (Hull City) right footed shot from outside the box is too high.
Foul by Robert Snodgrass (Hull City).
Jeff Hendrick (Burnley) wins a free kick in the defensive half.
Offside, Hull City. Jake Livermore tries a through ball, but Will Keane is caught offside.
Attempt missed. Andrew Robertson (Hull City) left footed shot from outside the box is too high. Assisted by Ryan Mason.
Tom Huddlestone (Hull City) wins a free kick in the defensive half.
Foul by Scott Arfield (Burnley).
Curtis Davies (Hull City) wins a free kick in the defensive half.
Foul by Patrick Bamford (Burnley).
Substitution, Hull City. Shaun Maloney replaces Sam Clucas.
Foul by Tom Huddlestone (Hull City).
Dean Marney (Burnley) wins a free kick in the defensive half.
Scott Arfield (Burnley) is shown the yellow card for a bad foul.
Robert Snodgrass (Hull City) wins a free kick in the defensive half.
Foul by Scott Arfield (Burnley).
Attempt blocked. Patrick Bamford (Burnley) left footed shot from outside the box is blocked. Assisted by Scott Arfield.
Substitution, Burnley. Patrick Bamford replaces Andre Gray.
Attempt missed. George Boyd (Burnley) left footed shot from outside the box misses to the left.
Curtis Davies (Hull City) hits the bar with a header from very close range. Assisted by Robert Snodgrass with a cross following a corner.
Corner,  Hull City. Conceded by Dean Marney.
Curtis Davies (Hull City) wins a free kick in the defensive half.
Foul by Andre Gray (Burnley).
Substitution, Burnley. Scott Arfield replaces Johann Berg Gudmundsson.
Substitution, Burnley. Jeff Hendrick replaces Steven Defour.
Substitution, Hull City. Ryan Mason replaces David Meyler.
Goal!  Burnley 1, Hull City 0. Steven Defour (Burnley) right footed shot from outside the box to the bottom right corner. Assisted by Dean Marney.
Substitution, Hull City. Will Keane replaces Adama Diomande.
Corner,  Hull City. Conceded by Tom Heaton.
Attempt saved. Robert Snodgrass (Hull City) right footed shot from the right side of the box is saved in the top centre of the goal. Assisted by Andrew Robertson.
Corner,  Hull City. Conceded by Matthew Lowton.
Attempt missed. Sam Vokes (Burnley) right footed shot from outside the box misses to the left. Assisted by Steven Defour.
Robert Snodgrass (Hull City) wins a free kick in the defensive half.
Foul by Stephen Ward (Burnley).
Robert Snodgrass scored a 95th-minute free-kick to rescue a point for Hull City in the Premier League at Burnley.