Scott Tiffoney put Partick ahead after 17 minutes, cutting in from the left and firing low at the near post.
Manny Duku hit the crossbar but the home side levelled through Kirk Broadfoot six minutes after the break when the defender shot into the bottom corner from the edge of the area. Shane Sutherland put Inverness ahead for the first time after 68 minutes and Aaron Doran added a third three minutes later when he fired into the top corner to complete the comeback.
Kilmarnock kept up the chase three points behind Billy Dodds’ side with a 1-0 win over Morton at Rugby Park with Rory McKenzie finding the net midway through the second-half.
The cinch Championship's highest scorers Arbroath moved third with their third win in five – a 4-0 victory over Hamilton. Scott Stewart broke the deadlock on the stroke of half-time when Accies goalkeeper Ryan Fulton failed to gather and within 12 minutes of the restart Michael McKenna drilled into the top corner for his sixth league goal of the season.
The situation got worse for the visitors when Jamie Hamilton was sent off for a high tackle on Stewart, and Arbroath took full advantage in the last 10 minutes, through Joel Nouble and Nicky Low.
Nikolay Todorov scored but Dunfermline remain bottom after losing 3-1 at Ayr United with Cameron Salkeld scoring between two Tomi Adeloye goals for Jim Duffy’s team.
Fife neighbours Raith Rovers lost at home to Queen of the South after Lee Connolly’s early goal.