Stuart Brannigan gave the home side the lead on16 minutes before they doubled their advantage after the break through Kris Doolan.
Motherwell stuck to their task and pulled a stunning goal back courtesy of Lionel Ainsworth but Partick retained their composure and restored their two-goal lead through Stephen O’Donnell.
Stuart McCall’s side created the first real opportunity of the match when Henrik Ojaama’s header was tipped onto the crossbar by Scott Fox before the Thistle keeper gratefully gathered the ball.
Steven Lawless went close to opening the scoring when he got the better of Stephen McManus before advancing and trying his luck from distance with a shot that fizzed just past the post of Well keeper Dan Twardzik.
Lawless was to play a key part in the opener though as he set-up Brannigan, who latched onto his pass before firing left-footed past Twardzik.
The goalmouth action became less frequent as the first half progressed, although Twardzik was forced to keep out a 20-yard volley from Doolan, with Motherwell’s best chance coming when Josh Law curled a shot over.
Thistle eventually doubled the lead on 63 through Doolan, who got ahead of Mark O’Brien before firing the ball into the roof of the net after Stephen O’Donnell had cut the ball back from the byline.
Motherwell stuck to their task and pulled a goal back through Ainsworth, who took a touch before unleashing a 40-yard drive that found the top-left corner.
But Partick retained their composure and restored their two-goal lead eight minutes from time on the counter-attack.
Substitute Nathan Eccleston won the ball ahead of Stuart Carswell on the touchline inside his own half and with Motherwell sub Zaine Francis-Angol out of position and Twardzik left unprotected, Eccleston fed the ball through to O’Donnell who calmly slotted home under the keeper.
Partick goalkeeper Fox then saved well from another substitute, Lee Irwin, in injury-time to leave Motherwell marooned in the bottom two.