Partick took the game to Kilmarnock and had the best of the early exchanges, taking the lead after 18 minutes when Kenny Milne found Jamie Mitchell and he was able to beat his defender and fire the ball low past Francois Dubourdeau into the far corner.
Killie equalised on 26 minutes when Stephen Murray beat Jean-Yves Anis to the byline and his cross found Colin Nish, who gave Arthur no chance from six yards out.
Thistle thought they were due a penalty on 29 minutes when Dubourdeau appeared to bring down Gerry Britton, but the referee waved play-on much to the forward's annoyance.
Both sides continued to make chances with Nish and Garry Hay coming close for Killie and Stuart Taylor just heading over for Thistle.
Despite these efforts there was no further scoring in the first half.
The second half started with Thistle pushing forward and they thought they had earned a penalty after 51 minutes as the referee appeared to point at the spot only to award a free-kick, much to the home side's fury.
It was Kilmarnock who took the lead on 61 minutes when, following a good passing move featuring Peter Canero, Murray and Nish, Gary McDonald was able to fire home from close range.
The same player extended Killie's lead after 66 minutes with a piece of individual skill which caught Kenny Arthur by surprise, when he back-heeled the ball into the net from eight yards out.
Thistle gave themselves a chance on 79 minutes when James Grady pulled a goal back. The Kilmarnock defence were unable to clear Derek Fleming's corner and Grady poked the ball home from close range.
Killie were not finished and made absolutely sure of all three points when Nish scored his second on 90 minutes, as he found himself unmarked at the back post and was able to fire the ball past Arthur from 14 yards.
All in all, another difficult day for Thistle but Kilmarnock will be delighted to take all three points from their travels.