Partick almost made the perfect start when, after only one minute, Gerry Britton got in front of his defender but saw his header from six yards out saved by the Livingston keeper Juan Broto.
Livingston recovered from this early scare and came back at Partick with Barry Wilson and Stuart Lovell both coming close after six minutes.
Livingston opened the scoring after 31 minutes when Phillipe Brinquins' speculative free-kick was met at the back post by the unmarked Oscar Rubio and his looping header went into the net via the underside of the bar.
Livingston were able to hold their lead for only one minute and Partick equalised when an Alex Burns corner was headed on by Martin Hardie to Jamie Mitchell who had the easiest of tasks of heading home from only a couple of yards out.
The second half started with Livingston in the ascendency with only a mixture of poor finishing and solid defending responsible for them not being able to add to the score.
Thistle at this stage were relying on long balls to their strikers and this tactic paid dividends after 63 minutes when they took the lead.
Burns collected a Hardie through ball and bore down on the Livingston defence.
His run was ended when Rubio brought him crashing to the ground inside the box. Mitchell scored from the resultant penalty.
This setback seemed to spur Livingston on and they had chances to equalise before they actually did so after 76 minutes when a Camacho cross was missed by all of the Thistle defence. It was met again by Rubio at the back post who was able to head home into an empty net.