Anthony Stokes' hat-trick ensured that holders Celtic progressed to the fifth round of the Scottish Cup at the expense of hard-working Peterhead.
The side sitting second-bottom of Division Three rarely threatened but bravely kept the score down.
Stokes tapped in when strike partner Georgios Samaras set him up in front of goal after 36 minutes.
The Irishman fired his second on the turn after 57 minutes and drilled another eight minutes from the end.
The only consolation for Peterhead, who had built temporary stands for the visit of the Scottish Premier League leaders, was a sell-out crowd and the breaking of their 3,700 record attendance.
Celtic manager Neil Lennon had made six changes, giving starts to Lukasz Zaluska, Cha Du-ri, Kelvin Wilson, Ki Sung-Yueng and Paddy McCourt along with Emilio Izaguirre as last season's player of the year continues his return from long-term injury.
And Zaluska was the first goalkeeper called into the action, nipping the ball off the toe of David Ross as the striker looked to finish off a fine passing move on the edge of the penalty box.
The Blue Toon's manager, former Celtic midfielder Jim McInally, had promised not to simply pack his defence and retained strikers Rory McAllister and Martin Bavidge in his unchanged starting line-up.
However, McInally altered his formation to five at the back as he looked to stifle high-scoring Scottish Premier League leaders who quickly showed their own menace when Stokes burst into the box and had a goalbound effort blocked.
Celtic's play was laboured and it was not until the 26th minute when they created a clear-cut chance, Stokes scooping a first-time effort over from 15 yards after Cha had thrust his way to the bye-line.
Ki was given acres of room on the edge of the box from a Charlie Mulgrew corner to crash a thundering drive off the crossbar.
Peterhead were now camped in their own half and goalkeeper Paul Jarvie did excellently to turn away a curling Mulgrew free-kick destined for the bottom corner.
However, Jarvie was left exposed in Celtic's next attack as Samaras burst past his marker into the box and turned it across the face of goal for Stokes to side-foot home.
Stokes sent a clever lob just over and was then caught offside as he turned a low Samaras cross into the roof of the net.
Celtic had been exploiting the space wide of the three in Peterhead's central defence and McInally attempted to counter that by bringing striker Bryan Deasley on for midfielder Graeme Sharp at half-time.
Stokes again had the ball in the net but was clearly offside before his clinical finish after being put clear by McCourt.
Celtic lost Joe Ledley to an injured cheekbone after 56 minutes, with Victor Wanyama his replacement, but the visitors made the game safe seconds later.
Stokes seemed to be moving away from goal when he swivelled superbly to bullet his drive from the edge of the box into the far corner.
Moments later, the Republic of Ireland striker went close to completing his hat-trick, having a low drive saved by Jarvie then slicing wildly wide from close range.
Celtic boss Lennon took the opportunity to give Filip Twardzik, whose twin Patrik is also on the Glasgow club's books, his debut in place of Samaras.
Peterhead finally had a shot on goal after 77 minutes, but Deasley's effort trundled well wide from 25 yards.
A twisting run into the box by substitute Dylan McGeouch caused havoc in the Peterhead defence and the move ended with Stokes firing the ball low into the far corner from 16 yards.
Live Text Commentary
Full Time The referee blows for the end of the match.90:00 +0:13
Ryan Strachan concedes a free kick for a foul on Dylan McGeough. Sung-Yeung Ki has a direct shot on goal from the free kick.89:11
Anthony Stokes is flagged offside by the assistant referee. Indirect free kick taken by Paul Jarvie.88:46
James Redman gives away a free kick for an unfair challenge on Filip Twardzik. Sung-Yeung Ki takes the indirect free kick.87:26
Roy McBain challenges Dylan McGeough unfairly and gives away a free kick. Du-Ri Cha takes the free kick.85:57
Kelvin Wilson concedes a free kick for a foul on Dennis Wyness. Ryan Strachan crosses the ball, Rory McAllister has a headed effort at goal from close in which goes wide left of the target.85:29
The referee blows for offside. Ryan Strachan restarts play with the free kick.85:00
Sung-Yeung Ki takes a shot. Comfortable save by Paul Jarvie.83:04
Inswinging corner taken by Filip Twardzik from the right by-line.82:52
The ball is delivered by Du-Ri Cha, clearance made by Ryan Strachan.81:22
Assist by Scott Brown.81:22 Goal scored
Goal! - Anthony Stokes - Peterhead 0 - 3 Celtic Anthony Stokes gets on the score sheet with a goal from inside the area to the top left corner of the goal. Peterhead 0-3 Celtic.80:51
Short corner taken by Sung-Yeung Ki.80:51 Substitution
Substitution Dylan McGeough on for Charlie Mulgrew.75:31
A cross is delivered by Emilio Izaguirre, Scott Ross makes a clearance.75:17
Sung-Yeung Ki decides to take a short corner.75:00
Anthony Stokes delivers the ball, clearance by Scott Ross. Scott Brown takes a shot from 20 yards. Dennis Wyness gets a block in.74:24
Sung-Yeung Ki takes a short corner.72:08
Bryan Beasley has shot on goal from just outside the box which goes wide of the right-hand upright.71:32
Filip Twardzik produces a left-footed effort from long distance that goes harmlessly over the bar.
The assistant referee flags for offside against Anthony Stokes. Ryan Strachan restarts play with the free kick.69:36 Substitution
Substitution Filip Twardzik comes on in place of Georgios Samaras.67:50
Free kick taken by Emilio Izaguirre.67:50 Substitution
Substitution Lewis Davidson on for David Ross.67:50 Booking
Booking Scott Ross is cautioned.67:42
Free kick awarded for an unfair challenge on Sung-Yeung Ki by Scott Ross.65:53
Scott Ross gives away a free kick for an unfair challenge on Anthony Stokes. Direct effort from the free kick comes in from Anthony Stokes.65:39
Centre by Du-Ri Cha, clearance by Roy McBain.63:52
Effort from just outside the box by Emilio Izaguirre goes over the bar.61:31
Sung-Yeung Ki decides to take a short corner.60:52
The ball is crossed by Du-Ri Cha, clearance made by Ryan Strachan.60:16
Kelvin Wilson takes the indirect free kick.60:16 Booking
Booking Rory McAllister goes into the referee's book for unsporting behaviour.60:07
Unfair challenge on Kelvin Wilson by Rory McAllister results in a free kick.59:27 Substitution
Substitution (Peterhead) makes a substitution, with Dennis Wyness coming on for Martin Bavidge.59:08
Effort from inside the area by Anthony Stokes misses to the left of the goal.58:53
Charlie Mulgrew takes the inswinging corner, James Redman manages to make a clearance.58:33
Anthony Stokes takes a shot. Paul Jarvie makes a save.57:14 Substitution
Substitution Victor Wanyama replaces Joe Ledley.56:32
Emilio Izaguirre provided the assist for the goal.56:32 Goal scored
Goal! - Anthony Stokes - Peterhead 0 - 2 Celtic Anthony Stokes grabs a goal from just inside the penalty area to the bottom left corner of the goal. Peterhead 0-2 Celtic.54:22
Scott Brown fouled by Bryan Beasley, the ref awards a free kick. Scott Brown restarts play with the free kick.51:03
A cross is delivered by Roy McBain.49:52
James Redman gives away a free kick for an unfair challenge on Scott Brown. Lukasz Zaluska restarts play with the free kick.47:49
The official flags Anthony Stokes offside. Paul Jarvie takes the indirect free kick.45:01
The second half has started.45:01 Substitution
Substitution Bryan Beasley joins the action as a substitute, replacing Graeme Sharp.45:00 +1:10 Half time
Half Time The ref blows to signal half-time.45:00 +0:52
The offside flag is raised against Martin Bavidge. Kelvin Wilson takes the indirect free kick.44:35
Free kick awarded for an unfair challenge on Anthony Stokes by Scott Ross. Charlie Mulgrew restarts play with the free kick.43:41
Centre by Scott Brown, save by Paul Jarvie.42:18
The ball is sent over by Georgios Samaras. Anthony Stokes is ruled offside. Paul Jarvie restarts play with the free kick.41:34
Foul by Kelvin Wilson on Rory McAllister, free kick awarded. The free kick is swung in right-footed by Ryan Strachan, Lukasz Zaluska makes a save.40:40
Effort on goal by Georgios Samaras from just inside the area clears the bar.39:22
Du-Ri Cha produces a cross, Ryan Strachan makes a clearance.38:05
The ball is delivered by Emilio Izaguirre, Ryan Strachan manages to make a clearance.36:37
Anthony Stokes is ruled offside. Indirect free kick taken by Paul Jarvie.35:27
Georgios Samaras provided the assist for the goal.35:27 Goal scored
Goal! - Anthony Stokes - Peterhead 0 - 1 Celtic Anthony Stokes gets on the score sheet with a goal from inside the area low into the middle of the goal. Peterhead 0-1 Celtic.33:54
Graeme Sharp concedes a free kick for a foul on Scott Brown. Charlie Mulgrew shoots direct from the free kick, Paul Jarvie makes a save.33:21
Free kick awarded for a foul by Scott Ross on Georgios Samaras. Direct free kick taken by Charlie Mulgrew.32:33
Patrick McCourt crosses the ball, clearance by David Ross.31:58
Sung-Yeung Ki takes a short corner. The ball is crossed by Patrick McCourt.29:05
Anthony Stokes gives away a free kick for an unfair challenge on David Donald. The free kick is delivered right-footed by Ryan Strachan from right wing, Charlie Mulgrew manages to make a clearance.27:53
Charlie Mulgrew takes the inswinging corner, Sung-Yeung Ki takes a shot.27:48
Du-Ri Cha crosses the ball, blocked by Martin Bavidge.27:01
Kelvin Wilson takes the indirect free kick.27:01 Booking
Booking The referee shows Roy McBain a yellow card.26:53
Foul by Roy McBain on Charlie Mulgrew, free kick awarded.26:07
Centre by Du-Ri Cha, Effort from deep inside the area by Anthony Stokes misses to the right of the goal.25:33
The ball is delivered by Emilio Izaguirre.21:29
Inswinging corner taken left-footed by Charlie Mulgrew played to the near post, clearance made by Martin Bavidge.21:22
Sung-Yeung Ki delivers the ball, Graeme Sharp gets a block in.21:18
A cross is delivered by Du-Ri Cha.19:21
Du-Ri Cha delivers the ball.18:24
Centre by Charlie Mulgrew, Ryan Strachan manages to make a clearance.18:02
Corner from right by-line taken by Charlie Mulgrew.17:07
The ball is swung over by Du-Ri Cha, James Redman makes a clearance.14:51
Anthony Stokes takes a shot. Callum MacDonald gets a block in.14:19
Anthony Stokes takes a shot. Blocked by Ryan Strachan.12:58
Free kick awarded for a foul by Callum MacDonald on Anthony Stokes. Direct free kick taken by Kelvin Wilson.11:56
Ryan Strachan takes the inswinging corner, Joe Ledley manages to make a clearance.11:34
Foul by Scott Brown on James Redman, free kick awarded. Free kick taken by Callum MacDonald.10:29
Anthony Stokes is caught offside. Paul Jarvie restarts play with the free kick.9:14
Centre by Graeme Sharp, Lukasz Zaluska makes a comfortable save.8:26
Scott Ross gives away a free kick for an unfair challenge on Anthony Stokes. Sung-Yeung Ki delivers the ball from the free kick right-footed from left wing, Ryan Strachan manages to make a clearance.6:29
James Redman gives away a free kick for an unfair challenge on Sung-Yeung Ki. Free kick taken by Charlie Mulgrew.5:53
The ball is swung over by Du-Ri Cha.4:56
Rory McAllister concedes a free kick for a foul on Scott Brown. Direct free kick taken by Kelvin Wilson.1:52
Foul by Rory McAllister on Georgios Samaras, free kick awarded. Free kick taken by Charlie Mulgrew.1:07
Rory McAllister takes a shot. Blocked by Kelvin Wilson.0:00
The ref blows the whistle to begin the match.
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