Celtic's quest for a domestic treble remains firmly on course after an impressive 2-0 win over Dundee in their William Hill Scottish Cup fifth-round tie at Dens Park.
Striker Leigh Griffiths headed the Hoops into the lead in the seventh minute with his third goal in four games and the home side were only still in the tie at the interval thanks to keeper Scott Bain.
The Scottish Premiership leaders, who face Dundee United in next month's Scottish League Cup final at Hampden Park, doubled their lead through midfielder Stefan Johansen at the start of the second half.
Paul Hartley's side, who went into the match unbeaten in their last six outings, struggled to live with the ferocious tempo set at times by the Hoops, especially in the first half, and could not find a way back into the match as the Parkhead side ultimately cruised into the quarter-finals.
And on this form Celtic might just fancy their chances in the upcoming Europa League last-32 tie against struggling Italian outfit Inter Milan.
They will be boosted for those matches by new signings from Dundee United, Stuart Armstrong and Gary Mackay-Steven, who were cup-tied against the Dark Blues on Saturday.
Manager Ronny Deila made only one change, bringing in wideman James Forrest for Anthony Stokes, who started on the bench.
Hartley, whose new signings Alex Harris and Paul Heffernan were cup-tied from their time at Hibernian, made three changes as Stephen McGinn, Luka Tankulic and Craig Wighton came in for Harris, the injured Kevin Thomson and David Clarkson, who dropped to the bench.
The game was still settling down when midfielder Nir Bitton picked out over-lapping right-back Mikael Lustig wide on the right and when he curled his cross into the middle Griffiths reacted quickest at the near post to glance a head past Bain.
It was a great start for Deila's side who moved forward with some pace and purpose in the search for a second.
In the 23rd minute, after skipper Scott Brown had a decent effort from inside the box deflected behind for a fruitless corner, Forrest should have doubled Celtic's lead.
The Scotland winger robbed Dundee skipper Gary Irvine in his own half and after playing a one-two with Johansen he found himself through on goal with only Bain to beat but the keeper blocked and the ball was scrambled to safety.
The Dees keeper made further close-range saves from Griffiths and Johansen as Celtic swarmed around the opposition penalty area.
For their part Dundee, who had to reshuffle when Greg Stewart limped off to be replaced by Paul McGinn, brother of team-mate Stephen McGinn, had only two real efforts.
A snap-shot from defender Kostadin Gadzhalov from the edge of the Celtic box whizzed past the post and just before the break, Hoops keeper Craig Gordon clawed away a deflected shot from former Parkhead midfielder Paul McGowan.
Kris Commons was replaced by Stokes for the start of the second half and one of the first things the Irishman had to do was congratulate Johansen.
A deep cross from Lustig found Griffiths unmarked at the back post and when his header was parried by Bain, the on-rushing Johansen fired the ball into the net.
As the mood among some of the home fans momentarily turned ugly, Lustig hobbled off to be replaced by Adam Matthews before Stokes was booked for simulation.
Clarkson was brought on for Wighton but there looked no way back for Dundee.
On the hour-mark Johansen curled in a cross from the right which a stretching Bain palmed on to the woodwork, relieved to see the ball stay out.
Stokes and Griffith had efforts either side of John Guidetti replacing Forrest and the match was controlled by the visitors all the way to the final whistle.
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