Goals from Jan Vennegoor of Hesselink, Scott McDonald and Shunsuke Nakamura eased Celtic past Irn Bru First Division bottom side Stirling Albion in their Scottish Cup fourth-round tie at Parkhead.
Netherlands international Vennegoor of Hesselink was in the right place to head a Lee Naylor cross past Beanos keeper Scott Christie with 37 minutes gone.
As Albion tired after the break, strikes from McDonald and Nakamura, playing for the first time since October after recovering from a knee injury, gave Celtic a scoreline their dominance deserved.
Nakamura's contribution was especially appreciated by the home fans, who gave him a standing ovation as he was replaced by Jim O'Brien immediately after firing in the third.
The match was preceded by a minute's applause for Phil O'Donnell, the former Celtic and Motherwell player who died after collapsing against Dundee United at Fir Park a fortnight ago.
Celtic beat Stirling 8-0 at Parkhead in a CIS Insurance Cup tie in 2001 and most of the Hoops fans were expecting an equally comfortable tie this time around.
Stirling midfielder Steven Bell was injured in the warm-up and replaced by former Celtic youth player Ross Harris, which should have added to the ease of the home side, who had new signing Andreas Hinkel making his debut.
But the first half was a bit of a slog until Vennegoor of Hesselink eventually broke the deadlock when he headed Naylor's cross in from around 10 yards out.
The home side moved steadily forward from the first whistle but their first attempt on goal came in the sixth minute when McDonald's volley from the edge of the box was saved by Christie.
Vennegoor of Hesselink fired wide from 16 yards out moments later while, at the other end, Stirling's lone striker David McKenna fired high over the bar with an ambitious effort from 35 yards.
But, almost inevitably, traffic continued towards the Stirling goal but Vennegoor of Hesselink and Aiden McGeady both failed with efforts.
Stirling boss Allan Moore raised his fists to the travelling fans in mock celebration when Ross Forsyth won his side their first corner of the game halfway through the first half but it came to nothing.
The breakthrough came after Naylor reached the byline for the first time in the match and fired his cross in to the unmarked Vennegoor of Hesselink.
The Dutch striker stooped to send a bullet header past the helpless Christie and with that goal Parkhead nerves were alleviated almost instantly.
McDonald had the chance to settle the tie seven minutes into the second half when the Australian international collected a pass from Massimo Donati 16 yards out but failed to connect properly and his shot trundled wide of the far post.
A subdued crowd shivered in the cold watching the Hoops control the game without having too much purpose to their attacks.
Scott Brown's turn and drive from the edge of the box, after Nakamura's free-kick from wide on the left had bounced around the Stirling penalty area, went inches wide of the post.
McGeady's wayward shot in the 57th minute, which finished up yards wide of the target, had less impact than his mazy dribble moments later which put Vennegoor of Hesselink through only for the Dutchman to be flagged offside.
In the 70th minute Naylor turned provider again when he drove into the Stirling box and cut the ball back for McDonald to calmly side-foot past Christie.
Moments later, Celtic goalkeeper Artur Boruc pulled off a terrific point-blank save from Albion defender Andy Graham, who latched on to a Stuart Devine free-kick just six yards from goal.
But Stirling were struggling now and five minutes later Nakamura fired in the third from the edge of the box with a ferocious left-foot drive. It was a trademark strike from the Japan international, who was warmly applauded as he went off the park to be replaced by O'Brien.
In the ensuing draw for the fifth round, Celtic were draw away to the winners of Airdrie United or Kilmarnock.
Scottish Cup fifth-round draw:
Morton or Gretna v Queen of the South
Falkirk or Aberdeen v Hamilton or Brechin
Airdrie United or Kilmarnock v Celtic
Hearts or Motherwell v Huntly or Dundee
Livingston or Cowdenbeath v Partick or Dunfermline
Hibernian v Rangers or East Stirlingshire
Cove Rangers or Ross County v St Johnstone or Raith Rovers
St Mirren v Clyde or Dundee United
Ties to be played on weekend of 2-3 February.
