Marley Watkins and Greg Tansey both struck as Inverness produced an impressive counter-attacking display in the opening half, before Lyle Taylor pulled a goal back for Partick.
Caley Thistle opened the scoring after 16 minutes at Firhill when Watkins found himself clean through and kept his composure to slot the ball into the net.
Either side of that strike, Watkins shot straight at Paul Gallacher and then slipped another effort past the post when one-on-one with the goalkeeper.
But the visitors doubled their tally on 27 minutes with a wonderful solo effort from Tansey, who skipped past three challenges and smashed his shot past Gallacher.
The home side looked solid after the break and almost pulled a goal back on 64 minutes, but Taylor was unable to squeeze the ball home during a scramble in the penalty area.
But the goal arrived three minutes later when Taylor latched on to a long ball from Stephen O’Donnell and crashed his shot beyond Ryan Esson.
Partick came close again 90 seconds later when Danny Seaborne rose to meet a Ryan Stevenson corner but sent his header wide.
Esson made saves from Christie Elliott and Seaborne as Partick pressed for an equaliser, while Ryan Christlie almost scored a third for Caley on the counter-attack.
But there was still time for another chance in the dying moments when Seabourne connected with a Stuart Bannigan free-kick, but Esson got his fingertips to the ball and secure the win for the visitors.