Wide man Robbie Fraser, on loan from Rangers, found space down the left and picked out Pittman, with the veteran midfielder slotting Davie Martindale's side into a first-half lead.
Arguably, it came against the run of play - after Thistle spurned chances through Graham and Robbie Crawford - but it should have been added to when winger Cristian Montano tried to lift the ball over home goalkeeper David Mitchell but got his angles wrong.
There was no such trouble for centre-half Wilson, who lashed in a second for the Lions soon after the break.
From there, Thistle - led by interim co-managers Mark Wilson and Graham - offered very little until centre-half Lee Ashcroft crashed a long-range effort off the crossbar and Graham uncharacteristically skied a shot over the bar with the goal at his mercy.
The Jags, once again, will have to come from behind in Friday’s second leg in West Lothian - live on BBC Scotland - if they are to reach the Premiership play-off final against the team who finishes 11th in the top flight.