The Spiders will face Hamilton Academical, Hibs and Livingston as well as the Jags in Group 3 of the competition and they were quickly into attack against their Glasgow rivals.
Lennon Connolly earned a corner in the second minute with Ricky Waugh’s deep set-piece going unconverted at the back post.
A minute later a surging run from Cammy Bruce took him deep into the Thistle box where he found McCormick who was eventually crowded out.
With 10 minutes played a fine ball from McLeish released Rocco Hickey-Fugaccia and the wide-man’s return ball just evaded the striker as he darted into the visitors’ box.
Hickey-Fuggacia was again in a good position on 21 minutes where he was picked out by Alex Fairlie who earned another corner for the young Spiders with Waugh’s in-swinging delivery again finding on takers.
Midway through the half Connolly progressed through the Thistle box thanks to a mixture of slick passing and smart dribbling however his parting shot was blocked.
Calum Ferrie was perfectly placed to save a 20-yard shot from Ricco Diack on 30 minutes as the Jags threatened to break the deadlock.
The opening goal came sixty seconds later minutes when Connolly fed the ball to McLEISH who turned away from his marker and found the far corner with a well-place drive.
It was almost two within a minute when Zach Mauchin cut a cross back to Hickey-Fuggacia and his first-time shot was net bound until Connor Storey stuck out a foot and diverted the ball wide.
From the resultant corner it was two nil as the ball was rolled to McCORMICK at the edge of the Thistle box and he picked his spot in the far corner and found it with a low shot.
Before the break McLeish sent a long-distance header over and a corner from Hickey-Fugaccia flashed just past.
Half-time: Queen’s Park 2 Partick Thistle 0
Seven minutes into the restart persistence from McLeish took him through two challenges and to eight yards out with his left foot parting shot drifting just wide of goal.
On 56 minutes a fine Crossfield pass from Mauchin allowed McCormick to release Bruce on the left and his low cross was flicked an inch over by McLeish and five minutes later Queen’s came close again as a through ball from Waugh found Connolly and he spun away from a Thistle defender before seeing a shot turned wide.
On 66 minutes Queen’s scored a third and it was an excellent goal as centre-back Lewis Reid played an inch-perfect defence splitting pass to McLEISH who took a touch before cracking the ball into the net.
Two minutes later it was four nil as CONNOLLY’s shot along the turf from 18 yards out found its way past Storey with the aid of a slight deflection.
Thistle looked to get back into things and on 72 minutes Jamie Taggart came in off the right wing and sent in a shot that Ferrie carefully watched as it cleared his goal.
With a quarter of an hour to go McLEISH completed his hat-trick as he was in the right place, just four yards out, at the right time to turn home a delightful cross from substitute Kane Thomson who had shown great skill to get to the by-line.
With two minutes to go Young Queen’s Park added a sixth goal and it was another well-worked effort as Christoper Mahon showed trickery and desire to send a ball across the Thistle goalmouth where THOMSON flicked it home.
Queen’s Park – Calum Ferrie, Zach Mauchin, Cameron Bruce (Joseph Smith 61), Will Tizzard (Archie Graham 46), Lewis Reid, Ricky Waugh, Rocco Hickey-Fugaccia (Andrew Lind 74), Lennon Connolly, Liam McLeish (Christopher Mahon 80), Alex Fairlie (Kane Thomson 74), Lucas McCormick.
Unused substitutes – Liam Russell (G/k), Benjamin Ferguson, Tyrece McDonnell.
Partick Thistle – Connor Storey, Toby Ferrie, Ji Stevenson (Ben McKenna 86), Matthew Monaghan, Wasiri Williams, Ben Williamson, Wes McDonald (Aiden McGinlay 70), Matthew Falconer (Cieran Loney 72), Ricco Diack (Ryan Gaughan 86), James Lyon, Jamie Taggart (James McFadden 86)
Unused substitutes – Luis Cameron (G/k)