Celtic 3 Greenock Morton 0
Moussa Dembele's second-half double and a late strike from substitute Odsonne Edouard gave holders Celtic a 3-0 William Hill Scottish Cup quarter-final win over Morton at Parkhead.
The well-organised Championship side proved stubborn and troublesome in the goalless first-half but their resistance was broken in the 62nd minute when Dembele headed in a Tom Rogic cross before winning and converting a penalty nine minutes later.
In the final minute fellow French attacker Edouard converted a James Forrest cross to take the Hoops into Sunday's last-four draw and another step towards a second consecutive treble.
German defender Marvin Compper, signed in January, made a belated Celtic debut after recovering from a calf injury.
Compper started his Hoops career in ignominious style, however, by passing straight to Ton attacker Gary Oliver, back in the side along with Frank Ross and Scott Tiffoney, but he was crowded out for a corner which Celtic defended.
However, the Greenock side, who had struggled with training all week due to the snow and ice, took confidence from Celtic's early indecision.
In the ninth minute veteran midfielder Gary Harkins, catching the eye with his languid style, fired a free-kick wide from 25 yards.
Celtic struggled to find their rhythm but in the 17th minute Dembele beat Morton goalkeeper Derek Gaston with a header from a Forrest cross only to see Morton skipper Thomas O'Ware head over from the corner.
The home side slowly began to build a head of steam and in the 37th minute, by which time Morton were mostly camped at the edge of their own penalty, Jozo Simunovic headed a Kieran Tierney corner past the near post.
Gaston then made two saves from Celtic midfielder Tom Rogic within a minute but again the corners came to nothing.
Edouard replaced Scott Sinclair for the start of the second half and within two minutes he fired straight at Gaston from 12 yards after getting the break of the ball.
The Parkhead side had stepped up the pace and Gaston parried a long-range effort from Olivier Ntcham past the post moments before the Ton goal was breached.
Following another Tierney corner, Rogic crossed back in for Dembele to head in off the crossbar from a couple of yards out.
Inside the last 20 minutes, Morton defender Michael Doyle was adjudged by referee John Beaton to have felled Dembele just inside the box - it looked like it could have been outside - allowing the Hoops striker to fire in his second.
Celtic relaxed in the final stages, as did Morton, who had little option but to push forward, stretching the game.
Dembele was denied his hat-trick in the 85th minute when Gaston tipped his header from a Forrest cross over the bar but when the Scotland international picked out Edouard 10 yards from goal, the on-loan Paris St Germain forward fired it high into the net to complete the win.