The home side lay siege to the Thistle defence at the start of the match but had to rely on a Kris Commons penalty a minute before the break to give them the interval lead.
Thistle midfielder James Craigen had been shown a straight red card for a ’last man’ foul on Hoops midfielder Stuart Armstrong to concede the spot-kick, leaving the visitors a player down for the second half.
Midfielder Stefan Johansen — stand-in skipper in the absence of suspended Scott Brown — added a second in the 63rd minute as the encounter turned into a Hoops procession.
With second-placed Aberdeen beating Inverness 1-0, Ronny Deila’s side maintained the gap over the Dons but also have a game in hand as the title race draws closer to conclusion.
Commons’ breakthrough goal came as some relief to the home fans who had grown slightly irritated as the first half wore on. Partick defended stoutly but were undone again when Johansen took a clever Guidetti pass before rolling the ball into the corner of the net from 10 yards.
Gordon, Matthews (Fisher 66), Denayer, van Dijk, Izaguirre, Biton, Johansen, Mackay-Steven, Commons (Forrest 66), Armstrong, Guidetti (Griffiths 75).
Fox, O’Donnell, Frans, Balatoni, Booth, Craigen, Bannigan (Fraser 77), Osman, Lawless (McDaid 58), Higginbotham, Stevenson (Taylor 55).