The hosts had recovered to lead 2-1 after conceding a very early goal but centre-back Frans then popped up to salvage a point for the visitors.
Partick got off to a fantastic start, taking the lead in the second minute when Kallum Higginbotham and James Craigen set up Ryan Stevenson, who produced a fine finish, shooting home left-footed from just outside the box.
The visitors almost added a second five minutes later when Kris Doolan arrived at the back post to get on the end of a Higginbotham corner but he put his header into the side-netting.
The hosts began to pose more of a threat as the half progressed and Sammy Clingan shot off-target from the rebound after Robbie Muirhead’s effort had been blocked.
Doolan then squandered another chance at the other end, missing his kick from Stevenson’s cross after a short-corner routine, Steven Lawless firing over when the ball fell to him.
And Killie drew level after 33 minutes through Josh Magennis, who finished off a counter-attack by shooting low into the net from distance after a lovely dribble and fine throughball from Rory McKenzie, who had won the ball back inside his own half.
That was the hosts’ first goal from open play for 742 minutes and they soon had the ball in the net again when Manuel Pascali got on the end of a Craig Slater cross, but it was ruled out for offside and the game was all-square at the break.
Partick began the second half on the front foot but Stevenson blazed a shot over the bar after some lovely build-up play.
Kilmarnock then had a loud shout for a penalty turned down when Muirhead tumbled to the ground in the box.
And the visitors took the lead in the 79th minute when Pascali turned the ball into the net at the back post after Partick were unable to clear a Slater corner.
But Thistle produced a quick response, pulling level in the 84th minute when a Stuart Bannigan free-kick was half-cleared, Declan McDaid volleyed the ball back, and Frans managed to divert it into the roof of the net from the edge of the six-yard box.
An entertaining encounter then finished with both sides pushing for a winner but Doolan was denied by a fine tackle and the teams had to settle for a point apiece.