Carl Tremarco scored a well-worked goal on the break to give the visitors a half-time lead.
That was extended early in the second period when Miles Storey's effort found the net via the post before Josh Meekings side-footed a third.
Kris Doolan's consolation gave home fans something to clap but Jordan Roberts notched a fourth for Caley.
It was an unusually abject performance from the Glasgow Jags, who were booed several times by their own fans and now sit six points ahead of the relegation zone with three games left.
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The match doubled as a bit of window shopping for Caley Thistle boss John Hughes, who has eyes for a few out-of-contract Partick players.
One of them is Steven Lawless, who should have done better with a left-foot shot that he dragged wide following some combative work by Ryan Edwards.
Partick's pre-match guide pointed out that the hosts had not scored a first-half goal at Firhill since 16 January, and it would be the visitors who hit the back of the net in the opening 45 minutes this time round in Maryhill.
Inverness broke on the counter attack with just under a quarter-of-an-hour gone and a fine pass by Andrea Mbuyi-Mutombo released Tremarco.
At first it seemed the Englishman was not sure what to do as he surged down the left, but he took the correct decision to plough on ahead and send a lovely finish into the far corner with the inside of his left boot.
Sean Welsh watched his free-kick well saved by the diving Owain Fon Williams in the Inverness goalmouth soon after.
Matters did not improve for the hosts after the break. Caley Thistle immediately extended their lead when Meekings found Storey at the right edge of the box. Hands were raised looking for an offside flag but the on-loan Swindon Town man focused on the task of hitting a shot goal-ward and in it went off the far post from a tight angle.
The Firhill crowd got even more uneasy when Roberts' close-range effort hit the post following good set-up play by Mbuyi-Mutombo, then Partick goalkeeper Ryan Scully had to pull off a great stop to deny Storey getting his second of the afternoon.
When Roberts' low drive narrowly missed the target moments later, the home support unleashed a barrage of boos.
Meekings did not miss, however. His controlled side-foot finish from Greg Tansey's corner made it three and very, very easy for Inverness.
Doolan did eventually manage to reduce the deficit, rounding Fon Williams after his initial effort was saved, but it did not take long for the visitors to restore their three-goal lead.
Richie Foran - who has had so many injury problems over the last two years - came on as a substitute and delivered a cross for Roberts to slam home at the back post and remind everyone which team had been in complete control.
Inverness Caledonian Thistle guaranteed Premiership safety by strolling to victory against Partick Thistle.