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.