Camilo Duran scored his first goal for Celtic as they won at Tannadice Park to secure their place in Sunday's quarter-final draw.
The Colombian striker fired into the net after Auston Trusty headed home from Benjamin Nygren's corner in the first half.
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Sebastian Tounekti fired low into the corner of the net, and Nygren curled in from the edge of the box to secure a comfortable win for last season's runners-up.
New signings Mika Baur and Haissem Hassan came on for their club debuts ahead of Wednesday's Champions League qualifier against LASK at Celtic Park.
Captain Kevin Nisbet's double set Aberdeen on their way to a comfortable 3-0 win over Dundee at Pittodrie.
Nisbet struck in the 51st and 63rd minutes and Mitchy Ntelo grabbed a debut goal in between as the Dons blew Dundee away after the break to book a place in the quarter-finals.
Dundee's cause was hampered by the loss of captain and striker Simon Murray to a knee injury during the first half of the second-round tie.
League One side Ross County shocked Dunfermline with a 2-1 win to progress to the last eight.
Richard Chin's late strike secured the victory after Liam Lindsay had put them ahead after the break.
Allan Oyirworth pulled Neil Lennon's Pars level with just 10 minutes to play, but Chin smashed the ball into the net in the 85th minute to secure County's place in Sunday's quarter-final draw.
Kilmarnock were first through to the quarter-finals on Friday night when Nicky Clescenco scored a dramatic late winner as they came from behind to beat Ayrshire rivals Ayr United 3-2.
Killie had suffered back-to-back defeats coming into the match and found themselves behind early on as Owen Stirton volleyed home before Joe Hugill equalised.
Ross Taylor's sublime finish then stunned the home fans but Michael Schjonning-Larsen scored an impressive solo goal of his own to make it 2-2 with 10 minutes remaining.
With the match seemingly heading towards an extra 30 minutes, the hosts completed the comeback when Clescenco showed superb composure to dink the ball home after Ayr goalkeeper Harry Stone had spilled a deep cross.
