Chris Erskine crossed low for Kris Doolan to tap home and give the Jags an early lead.
Adam Barton and Steven Lawless came close to doubling the hosts' advantage.
After a poor first half Well carved out chances to score in the second, Zak Jules's header kept out by goalkeeper Tomas Cerny.
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With one more round of fixtures to play before the Premiership splits in two, Thistle have a seven-point gap over Kilmarnock and will face Celtic, Aberdeen, Rangers, St Johnstone and Hearts in the final few weeks of the season.
Before then, they will visit Rangers next weekend, when Motherwell host basement side Inverness Caledonian Thistle.
Having come from a goal down to beat Ross County last week and drawing away to champions Celtic on Wednesday, Thistle's confidence was high and they were in a hurry to make that count.
Doolan scored both goals against County - his 100th and 101st for the Jags - and the striker marked being captain for the day with a simple finish off Erskine's ball across from the left.
Barton's free-kick drifted narrowly past the left-hand post and Lawless's shot was deflected on to the crossbar.
And Doolan should have got Thistle's second following an incisive pass by Ryan Edwards, the striker firing across the face of goal from the right of the six-yard box.
Other than an early Scott McDonald header that was blocked out for a corner, Motherwell failed to seriously trouble their hosts in the opening period.
Manager Stephen Robinson needed a reaction in the second half and sent on Keith Lasley and Lionel Ainsworth in place of Elliott Frear and Craig Clay.
Shea Gordon flashed the ball across goal but the stretching McDonald could not apply the finish, Cerny clawed away Jules's header and Lasley's effort did not trouble the Jags goalkeeper.
A late scramble in the box did not provide the telling shot at goal the visitors needed as Thistle held on, leaving Motherwell four points above Inverness and below Lanarkshire rivals Hamilton Academical on goal difference.
Lawless dragged a shot wide after driving at the Well defence but Alan Archibald's side struggled to create as many openings in the second half.
But one goal proved to be enough to ensure they will claim their highest top-flight finish since 1981.
They had been bottom of the division in December, a couple of months after Archibald stayed at the club following an approach by Shrewsbury Town.
He will now have the chance to get Thistle even higher in the Premiership with only three points separating the Jags from Hearts.
Match ends, Partick Thistle 1, Motherwell 0.
Second Half ends, Partick Thistle 1, Motherwell 0.
Niall Keown (Partick Thistle) wins a free kick in the attacking half.
Foul by Jacob Blyth (Motherwell).
Liam Lindsay (Partick Thistle) wins a free kick in the attacking half.
Foul by Ben Heneghan (Motherwell).
Attempt blocked. Jacob Blyth (Motherwell) right footed shot from the centre of the box is blocked.
Corner,  Motherwell. Conceded by Liam Lindsay.
Adam Barton (Partick Thistle) wins a free kick in the attacking half.
Foul by Keith Lasley (Motherwell).
Attempt missed. Carl McHugh (Motherwell) header from the centre of the box is close, but misses to the left.
Corner,  Motherwell. Conceded by Christie Elliott.
Foul by Andrew McCarthy (Partick Thistle).
Keith Lasley (Motherwell) wins a free kick on the left wing.
Substitution, Partick Thistle. Andrew McCarthy replaces Steven Lawless.
Attempt missed. Ben Heneghan (Motherwell) header from the right side of the six yard box misses to the right.
Corner,  Motherwell. Conceded by Ryan Edwards.
Adam Barton (Partick Thistle) wins a free kick in the defensive half.
Foul by Keith Lasley (Motherwell).
Foul by Adebayo Azeez (Partick Thistle).
Carl McHugh (Motherwell) wins a free kick in the attacking half.
Attempt missed. Keith Lasley (Motherwell) right footed shot from outside the box is just a bit too high.
Corner,  Motherwell. Conceded by Danny Devine.
Substitution, Motherwell. Jacob Blyth replaces Shea Gordon.
Attempt missed. Steven Lawless (Partick Thistle) left footed shot from outside the box misses to the right.
Attempt saved. Zak Jules (Motherwell) header from the centre of the box is saved in the bottom right corner.
Foul by Liam Lindsay (Partick Thistle).
Scott McDonald (Motherwell) wins a free kick in the defensive half.
Substitution, Partick Thistle. Adebayo Azeez replaces Chris Erskine.
Kris Doolan (Partick Thistle) wins a free kick in the attacking half.
Foul by Carl McHugh (Motherwell).
Attempt missed. Shea Gordon (Motherwell) left footed shot from the left side of the box is close, but misses to the right.
Liam Lindsay (Partick Thistle) wins a free kick in the attacking half.
Foul by Ben Heneghan (Motherwell).
Foul by Kris Doolan (Partick Thistle).
Stephen Pearson (Motherwell) wins a free kick in the defensive half.
Corner,  Motherwell. Conceded by Christie Elliott.
Ryan Bowman (Motherwell) wins a free kick on the left wing.
Foul by Niall Keown (Partick Thistle).
(Partick Thistle) wins a free kick in the attacking half.
Partick Thistle will finish in the Scottish Premiership's top six for the first time after beating Motherwell, who slipped to second bottom.