Aaah, the romance of the cup.

The most unsentimental of trysts yesterday took place at Balmoor Park amid a wind that would take the enamel from one's teeth, a cold that was an unanswerable riposte to daft notions of global warming and on a pitch that was as slick as Alex Salmond on eve of poll.

The assignation ended predictably with Celtic not quite loving Peterhead, but certainly leaving them behind.It was all sealed not with a kiss but a hat trick from Anthony Stokes that was more than enough to take Celtic into the fifth round of the William Hill Scottish Cup.

Peterhead, game and overly robust, initially made it an uncomfortable afternoon for Celtic, but never threatened to stretch or vex Neil Lennon's side beyond complaints about tackles. The afternoon was thus an occasion for the Celtic manager to assess his side in the expectation of tougher tasks to come rather than worry unduly about being dumped out of the cup.

The first start by Emilo Izaguirre since his ankle break in August was an obvious bonus and the Honduran had an energetic workout that will please both player and manager.

The other bonuses included the presentation of further evidence of the skill, tenacity and passing ability of Ki Sung-Yueng, surely destined for a major English Premier League club, the burgeoning assuredness of Charlie Mulgrew in central defence, admittedly against inferior opposition, and the endearing habit of Stokes to score goals despite infuriating team-mates with his occasional slackness in possession and in front of goal.

The only cause for a Lennon meditation, beyond a wince at some of Peterhead's tackling, was the performance of Paddy McCourt, restored to the first team in the absence through injury of Biram Kayal, and James Forrest through illness.

The Northern Irishman was consistently influential in playing in a quarterback position in front of the central defence. His range of passing, his ability to retain possession and his darting runs on the ball all contributed to an increasingly facile win.

Lennon has now joined that band of Celtic managers who cannot fail to be impressed by McCourt but who struggle to find space for him in their sides. The player yesterday gave persuasive evidence that he still has a role to play at Celtic Park and could contribute to the push for the three domestic trophies.

It was Stokes, though, with three goals, who claimed both the match ball and the headlines. His interventions rendered the afternoon a stroll for Celtic after a ponderous start against the second worst senior team in Scotland.

Peterhead, who have East Stirling to thank for not propping up the pyramid system of Caledonian football, tried to meet superior skill with brutal strength.

The home side launched into every tackle with the attitude that the Celtic player had just insulted the mass of Peterhead womanhood. Georgios Samaras, Stokes and Scott Brown all had cause to protest to referee Alan Muir as a series of wind-assisted tackles were launched in their direction. Roy McBain was eventually cautioned for a lunge on Charlie Mulgrew but not before Scott Ross, Rory McAllister and a posse of others had tested the official's patience. Ross and McAllister were eventually cautioned in the second half but the forbearance of the travelling Celtic support was more tested by the efforts of their side to impose themselves on the match in the early stages.

The treble by Stokes banished those early struggles into the wind but Cha Du-Ri should have created a succession of unmissable chances throughout the match as he was released almost routinely down the right flank through fine technique by Ki and McCourt.

However, the South Korean found a whole range of ineffective crosses. Stokes, too, contrived to squander good chances throughout the 90 minutes but, almost inevitably, he was the player to give Celtic the breakthrough in the 36th minute.

McCourt, sitting in front of his central defence and launching balls forward, found Samaras in space on the right with a long, ambitious pass. The Greek's ball across goal was knocked into a gaping net by Stokes.

It was a relief for Celtic. Notions of a cup upset had not been encouraged by a resilient Celtic defence but in attack only Ki's smashed shot off the bar and a Paul Jarvie save from a Mulgrew free kick had given intimations of a Celtic opener.

The first goal duly scored, Celtic strolled to victory in the second period. In the 57th minute, Stokes fired home after typically enterprising work from Izaguirre. He completed his hat trick when shooting strongly into the corner of the net after a good Celtic passing move that included a contribution from substitute Filip Twardzik.

Other chances were made and scorned but the result seemed enough to send the travelling Celtic support into a sustained burst of animated ecstasy at the end of the match. This may be ascribed to the romance of the cup but it is more likely the huddled mass was just trying to stay warm.