Adam Matthews first goal for Celtic helped the SPL champions past Arbroath and onward to a Scottish Cup fifth round tie with Raith Rovers.
The Glasgow side never got going during the replay and were lucky to be taken to extra time by the part-time outfit.
Arbroath’s player-manager Paul Sheerin made two changes from the side that drew with Stenhousemuir on Saturday, with Lee Sibanda and Paul Currie coming in for Connor Birse and Derek Holmes.
His opposite number Neil Lennon showed how much the game meant to him by bringing in three international players, Mikael Lustig, Beram Kayal and Georgios Samaras for Victor Wanyama, Joe Ledley and Gary Hooper.
Celtic were on the front foot early on as Samaras set-up Lassad Nouioui after a superb passing move, but unfortunately for the Tunisian he was flagged offside as he stroked the ball home.
After some pressure from the home side, Celtic eventually took the lead as Matthews stole the ball from Colin Hamilton before racing forward and unleashing an unstoppable effort which Morrison couldn’t reach as it nestled in the top corner.
Celtic’s front two continued to dominate, as Samaras got on the end of a long cross-field pass from Charlie Mulgrew and played a volley to Lassad, but Morrison managed to block the strike to prevent his side from going further behind.
Arbroath almost opened up the second half with an equaliser as Stuart Malcolm managed to get on the end of a Sheerin free-kick from the right wing, but unfortunately for the Red Lichties defender referee Craig Charleston saw a foul on Fraser Forster.
The visitors continued to push forward, with Scott Brown having a long-range effort which sailed wide of Morrison’s left-hand post.
Sheerin’s side nearly got level, as firstly Lee Sibanda almost got on the end of a cross from his boss, then a minute later Hamilton had the ball in the back of the net after Celtic keeper Forster dropped a corner, but once again the referee came to the English stopper’s rescue, awarding a free-kick in his favour.
The SPL leaders almost gave away an equaliser as Lustig failed to clear inside his own box, allowing Sibanda a strike at goal, but this time Forster was able to get behind the ball and clutch it to his chest.
Celtic should have wrapped up the tie when Morrison failed to deal with a cross, allowing Kayal a free header at goal, but the Arbroath stopper made up for his mistake, pulling off a stunning save.
Forster then matched his opposite number a minute later as Arbroath broke forward, with substitute Birse getting a one-on-one with the stopper, but he pulled off a superb save to deny the midfielder.
The part-timers continued to pressure their illustrious visitors, but couldn’t find a way past their defence to set-up another half an hour of football, allowing Lennon’s side to claim a fifth-round tie against Raith Rovers.