Thistle duly completed the group stages with a perfect record of four straight wins to leave manager Alan Archibald satisfied rather than ecstatic.
The Jags were pushed all the way in Glasgow’s “other derby” but ultimately their class and full-time fitness told.
Archibald said: “I’m happy with the result but I thought it was a bit slow at first and a bit like a pre-season game.
“They had a couple of good chances early on and thankfully we had Tomas (Cerny) back to show what he could do. We knew it would be a tough game because Gus (MacPherson) made Queen’s Park hard to play against.
“But overall the players have done what we asked them and we’re seeded for the next round which is important.
“The players have enjoyed the new format and we’ve been fortunate because we’ve had good crowds at all our games.”
Thistle survived an early scare when the Spiders carved out an excellent chance following a swift break down the right.
Ross Millen’s cross was perfectly measured for Aiden Malone whose header was brilliantly parried by Cerny at point-blank range before Ziggy Gordon booted the ball to safety.
And the Jags cashed-in on the let-off by racing upfield to take the lead through a looping Chris Erskine header that left Andrew Murphy stranded.
They almost doubled their lead when wing-back Gordon jnked inside his marker before curling a left-foot shot just wide of the far post before an Erskine shot was deflected for a corner as the Firhill men began to dominate.
However, Queen’s Park were quick to attack at every opportunity and they threatened for a second time when Darren Miller’s free kick was glanced goalward by Adam Cummins who was only denied by another athletic save from Cerny.Thistle continued to dominate possession without finding a cutting edge to some intricate build-up and instead Cerny was forced into action again following an enterprising run and shot from Josh Watt.
At the other end Kris Doolan showed excellent control to gather Liam Lindsay’s long pass before seeing his rising shot tipped over by Murphy.
Thistle produced the move of the match early in the second half when Erskine released substitute David Amoo whose pinpoint cross was headed inches wide by David Wilson.
Queen’s responded to force a corner from which Cummins headed Miller’s delivery over the bar.
But Thistle were even closer when Amoo crossed for Ade Azeez whose close-range header hit the bar and bounced over.
Amoo and Erskine then saw efforts deflected behind as the Maryhill men searched for a second clinching goal and it came when Erskine’s corner found Liam Lindsay rising above the visiting defence to head home.
Finally Partick could breathe a little easier and they almost emphasised their superiority when Azeez saw his point-blank effort brilliantly blocked by Murphy.
Archibald paid tribute to man-of-the-match Erskine, adding: “He brings an urgency and a drive and you know what you’re going to get from him.
“He is also very versatile as are all the players so we’ll be able to rotate. But the real test for us comes next week.”
Queen’s Park’s head coach Gus MacPherson made no comment after the match.