Martin O'Neill's side secured their place in the fourth round of the Scottish Cup as Stranraer's hopes of staging a giant killing were washed up on the west coast.
The Second Division outfit had hoped the Glasgow giants would find it difficult to get into their stride, however, they got the total opposite from the rampant visitors - a professional display from the SPL leaders and a comfortable victory.
Goals from Joos Valgaeren, Jackie McNamara, Lubo Moravcik and an own goal from Keith Knox sent the 2,300 Celtic supporters packed into Stair Park home to Glasgow and across the water to Ireland happy.
The Stranraer fans would have also gone home satisfied last night after a late goal from Ian Harty, but promotion remains their main objective.
Celtic took control from the start and got back in the groove after their winter break. With no sign of rust they carved out a glorious opening as early as the second minute.
Henrik Larsson headed Ramon Vega's cross on target, but Stranraer's goalkeeper Mark McGeown got down low to his left to deny the Swede.
Stranraer, however, gave their millionaire opponents an almighty scare in the 15th minute following a rare foray into the Celtic half. Paul Walker cut inside Valgaeren before unleashing a right-footed effort which Robert Douglas did well to save.
But Celtic eased any nerves when they took the lead in the 24th minute.
Vega once again appeared at the far post to head Lennon's free-kick goalwards. It was destined for the back of the net - but Valgaeren made sure by heading home from close range.
Celtic doubled their lead in the 51st minute when Chris Sutton played the ball inside to Larsson who squared it to McNamara to blast home an unstoppable shot.
Celtic refused to rest on their two-goal cushion and just five minutes later they got a third goal. Petta's dangerous cross was fired into his own net by Knox - who was sporting a bandaged head after sustaining a cut following a collision with Vega.
Celtic rubbed salt in the Stranraer wounds when they brought on two international stars in the shape of Paul Lambert - making his first appearance since being injured in November - and Moravcik, for Petta and Larsson.
The home supporters did have something to celebrate in the 84th minute when Alan Thompson was dispossessed by Harty, who crashed a fierce right-footed effort past Douglas.
Celtic, however, had the final say when Moravcik picked the ball up in the middle of the Stranraer half before hitting a tame shot which squeezed under McGeown's despairing dive and over the line.
Stranraer: McGeown, Johnstone, Wright, Knox, George, Hodge, Blair, Billy McDonald, Harty, Jenkins (Bryce 70), Walker. Subs Not Used: Jered Stirling, Geraghty, Rae, O'Neil. Booked: Knox, Blair. Goal: Harty 84.
Celtic: Douglas, Boyd, Petta (Lambert 61), McNamara, Valgaeren (Mjallby 65), Vega, Lennon, Agathe, Larsson (Moravcik 61), Thompson, Sutton. Subs Not Used: Smith, Gould. Goals: Valgaeren 23, McNamara 51, Knox 55 og, Moravcik 85.
Referee: S Dougal (Scotland).
