Kris Doolan and Conrad Balatoni scored two headers in the opening nine minutes to give Alan Archibald's men complete control.
Stuart Bannigan's long-range effort then made sure of the points midway through the second half, as Thistle moved nine points clear of the bottom two.
St Mirren, meanwhile, remain rooted to the foot of the table as substitute Lee Miller's late strike for Kilmarnock inflicted another damaging defeat.
The striker swept home Josh Magennis' square ball just three minutes from time to prevent St Mirren climbing above Motherwell on goal difference.
The result extended Gary Locke's side's unbeaten run to seven league matches.
Hamilton's winless sequence now stands at 10 matches, after they squandered a two-goal advantage to draw 2-2 against Ross County.
Jason Scotland and Dougie Imrie put the hosts two up inside 18 minutes, but Craig Curran pulled one back before the break and Michael Gardyne equalised in the 71st minute.
