The Jags threw the race to avoid a relegation play-off wide open when Taylor-Sinclair nodded home from six yards following a cross by Kallum Higginbotham.
The goal offered redemption for the defender, whose error had allowed on-loan Brighton player Vitaljis Maksimenko to fire his first goal in British football in the 53rd minute.
The lead lasted just three minutes before Higginbotham got the goal his performance thoroughly merited as he netted from a free-kick.
Killie thought they had scored in their next attack but referee Brian Colvin ruled Michael Gardyne's shot had bounced outside the goal after his long-range strike hit the crossbar.
Thistle got back on top and their enterprise - and left-back Taylor-Sinclair's desire to get forward - was rewarded as they moved level on points with Killie in an increasingly tight battle to avoid the play-off, with Ross County slipping down.
The visitors looked a side determined to get out of danger as they created a string of early chances, the first two from Higginbotham set-pieces.
James Craigen fired an acrobatic volley off the bar from 12 yards after a header on by Conrad Balatoni, who soon got in front of Manuel Pascali following a corner but headed over from six yards.
Kilmarnock goalkeeper Craig Samson then flew to his right to touch Kris Doolan's 25-yard strike over the crossbar.
There were only 12 minutes on the clock by then and an agitated home support transferred their nerves to their team, despite manager Allan Johnston's decision to plump for experience ahead of youth by replacing Craig Slater and Robbie Muirhead with Pascali and Gardyne.
Doolan was inches away from Higginbotham's cross and Thistle failed to make the most of a dangerous break.
The home side belatedly created some chances but Kris Boyd headed on to the roof of the net following a corner and was then foiled by goalkeeper Paul Gallacher's speed off his line after nicking a long ball past Lee Mair.
The PFA Scotland Player of the Year nominee then missed a sitter as he scuffed Gardyne's cutback with Gallacher out of position.
Thistle again started with purpose after the interval and Prince Buaben fired just wide from long range.
But Kilmarnock looked in more determined mood following the half-time team talk and Rory McKenzie set up Jackson Irvine but Gallacher stood firm at his near post to stop the shot.
And Killie were soon ahead after Taylor-Sinclair made a mess of clearing Alexei Eremenko's deep corner. The ball fell for Maksimenko and the Latvia international swept it inside Gallacher's near post from close range.
Thistle immediately hit back after Pascali fouled Chris Erskine 22 yards out. Higginbotham took aim and curled a low free-kick just inside Samson's left-hand post.
The home side thought they had regained the lead moments later when Gardyne chipped Gallacher from 30 yards. The ball hit the underside of the bar and bounced down with Killie claiming a goal but the grounded Gallacher scooped the ball away despite pressure from McKenzie and play continued amid protests.
Irvine then set up chances for Ross Barbour, whose effort was cleared off the line by Balatoni, and Gardyne, who glanced a header wide.
But Thistle began to pile men forward, and substitute Lyle Taylor fired wide under pressure from Maksimenko, before Taylor-Sinclair ran untracked into the six-yard box to send the away fans wild.
They still needed Gallacher to secure the three points as the keeper pulled off an excellent stop to push away Barbour's dipping volley.