Odsonne Edouard scored the opener as Celtic continued their resurgence with a 3-2 Premier Sports Cup win over Hearts that was more comfortable than the score suggests.
Edouard - back in the starting line-up as centre-forward after Ryan Christie missed out with a minor injury - finished off a slick attack in the 29th minute.
Kyogo Furuhashi moved out to a wide left position to accommodate the Frenchman but he linked up with Edouard to set up Stephen Welsh to head the second, and the Japan international restored Celtic's two-goal cushion in the second half.
Carl Starfelt had gifted Liam Boyce the chance to get Hearts back in it from the penalty spot, and substitute Aaron McEneff pulled a goal back in stoppage-time. But Celtic goalkeeper Joe Hart otherwise enjoyed a quiet afternoon as the hosts dominated possession.
Full Scottish league Cup quarter-final draw...
- Celtic v Raith Rovers
- Rangers v Livingston
- Dundee United v Hibernian
- Dundee v St Johnstone
Aberdeen crash out at Raith Rovers
A much-changed Aberdeen side crashed out after a second-half collapse against Raith Rovers.
Jay Emmanuel-Thomas gave the Dons an early lead and they utterly dominated possession in the first half.
But on-loan Stoke striker Ethon Varian netted just after the restart and Raith took the initiative before Dario Zanatta struck in the 71st minute to earn a 2-1 second-round victory.
Aberdeen's response was too little, too late and there was further misery for Stephen Glass as he saw Jonny Hayes and Ryan Hedges go off injured in the latter stages.
Hibernian bounce back from Euro exit
Hibernian bounced back from their European exit to reach the quarter-finals with a 2-0 victory over Kilmarnock.
Kyle Magennis and Kevin Nisbet found the net in the second half against the Championship side as the Leith outfit showed no signs of fatigue from a demanding run of games.
Kilmarnock had to soak up pressure for large spells of the game but did go close in the first half through Liam Polworth, whose drive bounced down from the underside of the bar before being cleared.
The only blot on an otherwise productive afternoon for the hosts was the pre-match confirmation that striker Christian Doidge would be sidelined for at least three months with an Achilles injury he sustained in training just the day before Thursday's 4-1 Europa Conference League defeat to Croatians HNK Rijeka.
Holders St Johnstone into the last eight
Holders St Johnstone progressed after twice coming from behind to defeat Arbroath 3-2 on penalties after Sunday's thrilling encounter ended 2-2 following extra time.
Ricky Little missed the first penalty for the Championship side and their chances appeared to be over when Dale Hilson missed the target, but Jason Kerr and Callum Booth both failed to convert for Saints.
However, Bobby Linn hit the post for the hosts and Ali McCann wrapped up the Perth side's win.