But Killie produced a spirited second-half display at Firhill, having been dominated in the first half, and Kris Boyd's 47th minute header earned them a share of the spoils.
Partick had the ball in the net after just five minutes through a close-range Kris Doolan effort but the goal was disallowed because of handball in the build-up.
However, the hosts did not have to wait long to take the lead, Aaron Muirhead (11) scoring confidently from the penalty spot after Manuel Pascali was penalised for a high challenge on Steven Lawless.
Thistle continued to hold sway and Lawless tested Craig Samson with a half-volley and then narrowly missed the target with a curling effort.
And Samson also pulled off a superb reflex save to turn a very well-struck Doolan effort around the post.
Kilmarnock then produced their best move of the opening half and it ended with Barry Nicholson heading wide from a Sean Clohessy cross.
Pascali then had a shot saved by Scott Fox but Partick went close again, in between those chances, Samson tipping a Kallum Higginbotham header over the bar.
Kilmarnock hit back
However, Kilmarnock made a flying start to the second-half, Boyd getting on the end of a Clohessy cross and beating Fox with a fine header.
Boyd almost scored again moments later but Fox pulled off a tremendous save this time after the striker had been found by Michael Gardyne.
The busy Fox then pulled off another great stop, denying Ismael Bouzid when the Killie man met a Nicholson corner.
And Boyd then threatened yet again, shooting just over the crossbar from 25 yards out, but the hosts were also chasing a winner and Doolan got on the end of a nice pass over the top, only for his low shot to be saved by Samson.
Partick substitute Christie Elliot then latched onto a pass from Aaron Sinclair and was unlucky to see his shot from the edge of the box come back off the post.
Sinclair whipped a cross through the box, Doolan not quite able to get on the end of it, before Elliot went close once more with just four minutes left, only for Samson to produce another smart save.
And Killie sub Mark Stewart made a great challenge in stoppage-time to foil Elliot and ensure both sides finished with a point.