Match ends, Clyde 0, Celtic 3.
Celtic maintained their dreams of a fourth consecutive domestic treble as they strolled past League One Clyde and into the Scottish Cup last eight.
Neil Lennon's side also exacted revenge for a shock cup defeat at Broadwood Stadium back in 2006, with their 12th away win in a row.
Olivier Ntcham and Scott Brown gave Celtic a commanding half-time lead.
Vakoun Bayo added a third late on as the holders comfortably sealed their place in the quarter-finals.
The draw, which took place after the tie, gave Celtic a trip to St Johnstone in the last eight.
Celtic exorcise Broadwood memories
The Miracle at Broadwood of 2006 was never likely to be repeated and, despite the best efforts of a howling wind to disrupt the spectacle, Celtic produced a dominant, professional display without really hitting the heights they can.
Clyde started brightly in front of a packed crowd, with neither side threatening either goalkeeper in the initial stages. Gradually, Celtic began to stretch their hosts and the breakthrough arrived in style.
Ntcham, whose goalscoring threat, passing range and strength were evident throughout the first half, gathered on the angle of the box, cut back and fired a crisp shot across Clyde goalkeeper David Mitchell into the far corner. A goal of great technique on his 24th birthday, it gave Celtic the platform they sought.
Ryan Christie fizzed one from distance narrowly wide before a sensational move released Patryk Klimala through on goal. He looked certain to score on his first start but Mitchell raced from his line to produce a magnificent save.
The crucial second arrived when Ntcham did well to force a corner. Klimala managed to flick it towards the front post where captain Brown outmuscled his opponent to poke home.
Celtic camped in Clyde's half for much of the second period without breaching the opposition too often. Christie did clip the bar in the dying stages before Moritz Bauer found space and squared for substitute Bayo who slotted home.
Credit to the hosts, they were far from embarrassed, put on a creditable show and almost nicked a late consolation through David Goodwillie, who perhaps ought to have squared for Ally Love to tap in.
The game meant much more to Clyde than what happened on the pitch and they were not overrun as Lennon's squad took another step closer to retaining the trophy.
'We more than matched them' - reaction
Clyde manager Danny Lennon: "The simplicity in the way Celtic plays is very good, and I thought they had a very good disciplined performance. We more than matched them in the second-half, but quality is always going to come through."
Celtic assistant manager John Kennedy: "We felt comfortable, it was a controlled game - the boys were professional. We'd have liked to have scored more goals but Clyde defended well and stayed in a good shape."
- 2HowieBooked at 79mins
- 7CuddihySubstituted forJohnstonat 85'minutes
- 8McStaySubstituted forCunninghamat 69'minutes
- 11LamontBooked at 24minsSubstituted forLoveat 79'minutes
- 49ForrestSubstituted forHayesat 71'minutes
- 27ElyounoussiSubstituted forShvedat 85'minutes
- 11KlimalaSubstituted forBayoat 75'minutes
- Bobby Madden
- Shots on Target
Second Half ends, Clyde 0, Celtic 3.
Attempt blocked. Ryan Christie (Celtic) right footed shot from the left side of the box is blocked.
Attempt missed. David Goodwillie (Clyde) right footed shot from the right side of the six yard box misses to the left.
Goal! Clyde 0, Celtic 3. Vakoun Issouf Bayo (Celtic) right footed shot from the centre of the box to the centre of the goal. Assisted by Moritz Bauer.
Attempt missed. Moritz Bauer (Celtic) right footed shot from the right side of the box is too high.
Attempt blocked. Scott Brown (Celtic) right footed shot from outside the box is blocked.
Ryan Christie (Celtic) hits the bar with a left footed shot from outside the box.
Attempt missed. Ryan Christie (Celtic) left footed shot from outside the box is close, but misses the top left corner.
Substitution, Clyde. Chris Johnston replaces Barry Cuddihy.
Substitution, Celtic. Marian Shved replaces Mohamed Elyounoussi.
Attempt missed. Vakoun Issouf Bayo (Celtic) right footed shot from the right side of the box is close, but misses to the right.
Attempt blocked. Vakoun Issouf Bayo (Celtic) right footed shot from the left side of the box is blocked.
Corner, Celtic. Conceded by Tom Lang.
Foul by Boli Bolingoli-Mbombo (Celtic).
Craig Howie (Clyde) wins a free kick in the defensive half.
Substitution, Clyde. Ally Love replaces Mark Lamont.
Craig Howie (Clyde) is shown the yellow card for a bad foul.
Boli Bolingoli-Mbombo (Celtic) wins a free kick in the attacking half.
Foul by Craig Howie (Clyde).