The Jags held their SPL opponents to a deserved 1-1 draw and earned a replay at Firhill.
Rangers started the game in sluggish fashion but still managed to take the game to Thistle early on with Nacho Novo sending a 25-yard effort narrowly wide of Jonathan Tuffey's right-hand post.
Then in the ninth minute, cup final hero Kris Boyd headed over the crossbar from Kirk Broadfoot's cross.
Thistle responded with a shot from midfielder Scott Chaplain which drifted wide and, in fact, it was the visitors who manufactured the best chance of the half when on-loan Hibs striker Damon Gray broke through on the right before firing in a low angled shot which was scrambled to safety by Allan McGregor.
Rangers were struggling to cope with the enthusiasm which was being shown by their lower division opponents and the restlessness of their supporters was becoming increasingly apparent as half-time approached.
However, their spirits were lifted four minutes from the break when Broadfoot's powerful header was superbly saved by Tuffey.
Novo then headed wide from Broadfoot's cross as the first half stuttered along to a goalless conclusion.
Clearly rattled by the unexpected resilience which had been shown by their Glasgow neighbours, Rangers began the second half aggressively and, after forcing a succession of corners, they came agonisingly close to taking the lead on 51 minutes when Steven Naismith saw his close-range header rebound off the crossbar.
Remarkably, it was the Jags who took the lead midway through the second half when Gray latched onto a superbly weighted pass from Chaplain before clipping his shot past McGregor from a tight angle.
Gray was then yellow carded for his over exuberant celebrations with the Thistle fans packed behind the goal at the Broomloan end of the stadium.
But the lead lasted a mere two minutes as Rangers equalised with a close-range effort from Boyd after Tuffey had saved well from substitute Chris Burke.
Rangers pressurised the Thistle goal incessantly for the final 20 minutes, but Ian McCall's men held out for a draw and fully merited the result which keeps their participation in the tournament alive.