Kevin McCann, the right-back on loan from Hibernian, broke the deadlock with a terrific strike from distance 11 minutes before the break.
Adam Rooney coolly slotted home the second after 51 minutes before Russell Duncan added a spectacular third with an audacious half-volley three minutes later.
Rooney rounded off the scoring with a penalty after 82 minutes as United's Europa League exertions against AEK Athens appeared to have caught up with them.
The hosts kept faith with the same starting XI that lost 1-0 to AEK on Thursday with midfielder Danny Swanson again missing out with an Achilles injury, while former Caley defender Darren Dods had to be content with a place on the United bench.
Thistle boss Terry Butcher, without injured captain Richie Foran, made one change from the side that lost to Celtic last weekend with David Proctor stepping in to replace right-back Ross Tokely.
The visitors made a lively start but Eric Odhiambo, who had an unsuccessful stint on loan at Dundee United back in 2008, saw his low drive comfortably gathered by Dusan Pernis before Rooney rifled a shot past the post after seven minutes.
United created their first opening after 11 minutes when Morgaro Gomis found David Goodwillie with an intelligent pass but the young attacker blasted high and wide.
Prince Buaben created a yard of space for himself on the edge of the area with a neat turn to dart away from Russell Duncan, but the Ghanaian's powerful shot deflected off Grant Munro for a fruitless corner.
United almost broke the deadlock after 27 minutes when skipper Jon Daly was only inches away from connecting with an enticing Craig Conway corner.
At the other end, Rooney twisted Garry Kenneth inside and out but Slovakian stopper Pernis was equal to his left-footed shot.
Inverness were growing in confidence as the half wore on and opened the scoring in spectacular fashion after 34 minutes.
A Jonny Hayes corner was headed clear as far as McCann, who unleashed an unstoppable drive from all of 30 yards that gave Pernis no chance.
Caley were claiming for a penalty within two minutes of the restart when Hayes fell under pressure from Paul Dixon in the box but the United left-back looked to have won the ball first.
Hayes should have doubled his side's lead soon after when he was released by Rooney but the winger dragged his shot wide.
But the inevitable second came after 51 minutes when Odhiambo easily turned Kenneth before teeing up Rooney who slotted home from the edge of the area.
And the noisy travelling support were treated to a sensational third three minutes later when Duncan pulled off an audacious first-time shot from a McCann throw-in which sailed over Pernis and into the top corner.
The visitors had the chance to score a fourth with eight minutes remaining when Rooney was clumsily brought down in the area by Kenneth.
The Irishman dusted himself down before slamming the ball past Pernis with many of the home support deciding they had seen enough and heading for the exit.
Buaben was unfortunate not to add a consolation goal for United in the closing stages when his neat volley rebounded back off the post.