The contest looked set to be heading straight to a penalty shootout when Lewis Stewart grabbed his second goal of the game for the Gers in stoppage time, but the home side had the final say when Matthew Falconer’s free-kick found the top corner minutes later and Thistle added a fifth goal of the contest on the counter-attack.
It means the Light Blues bow out of the competition in the Third Round following back-to-back final appearances.
Thistle got the scoring underway in Springburn when a deep delivery to the far post from a corner cannoned off the back of full-back Arran Kerr and into the Gers goal.
Indeed, the away side had been forced into an early change between the posts when Alfie Halliwell went down in some discomfort and was replaced by Greig Thackray.
Josh Gentles was denied by the upright as the Light Blues searched for a response, while Stewart passed up a dangerous opportunity on the counter-attack when the ball was played square by Callum Burnside.
The visitors, however, found a leveller before the interval when neat work from Burnside saw the teenager’s effort fall back the way of Stewart who steadied himself and finished into the bottom corner.
Only seven minutes had elapsed in the second period when Thistle restored their advantage through a first-time Chris MacKay finish.
There was no time to be licking wounds for Rangers and their response was almost immediate when Josh Gentles danced his way into the penalty area and, when the opportunity opened up, he placed a delicious finish into the far corner.
However, Rangers’ set-piece woes continued as the hosts took the lead for the third time in the contest from a free-kick delivery, leaving the Light Blues with it all to do to save their cup campaign.
The Gers thought they had salvaged the contest in stoppage time when Stewart latched onto a pass from Chris Eadie following a lapse in the Thistle ranks, coolly slotting the ball into the bottom corner with only the goalkeeper to beat.
But there was still more drama to come as Thistle raced down the opposite end from kick-off and won a free-kick on the edge of the area which Falconer dispatched into the top corner.
With bodies pushed into the hosts’ half, Thistle spotted an opportunity on the break to put the tie to bed and they duly did so with a finish into the bottom corner.
PARTICK THISTLE: Storey, Rooney, Low, Monaghan, Johnston (Waddell, 67), Dolan, Gaughan (Braid, 82), Falconer, MacKay (Paterson, 82), Docherty (Fullerton, 64), McKenna
Subs not used: Cameron, Williamson
RANGERS: Halliwell (Thackray, 9), Kerr, Wyllie, Campbell, Scott, McClure (Smith, 80), McCallion, Gentles, Stewart, Burnside, Eadie
Subs not used: Caldwell, Leitch, Crilly, Fernie, Wark