NEIL LENNON'S advice was that his players would need to be professional and adapt to the circumstances if they were to avoid a second cup upset in the space of a week.

They clearly listened.

Celtic are into the quarter-finals of the William Hill Scottish Cup, in which they will travel to face St Mirren, but it took a disciplined and patient performance to finally wear down a dogged Raith Rovers side who seemed intent on sitting in and scrapping for what would have been, for them, a fairly lucrative replay.

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This was Celtic's first visit to Stark's Park since 1997 and they will not be desperate to go back in a hurry, even if they eventually secured the result for which they were looking. This was cup football the old-fashioned way, a rutted pitch and a blustery wind combining to make seasoned internationalists look foolish.

Balls they expected to run on would stop dead on a divot or ricochet in unforeseen directions. Simple passes to team-mates would catch a gust and fly five metres past. Crosses would go up in the air and hang there, before dropping suddenly.

Celtic were the dominant team throughout but the conditions perhaps helped place a seed of uncertainty in their minds. Patience and perseverance were therefore key to their success – especially with Raith showing no great inclination to leave their own half until late in the game – and Celtic were eventually rewarded with three second-half goals that secured their passage into the last eight.

The first arrived via a penalty decision that Simon Mensing later insisted was wrong, and that Lennon conceded might have been "soft". Mensing, one of Raith's best players on the day, did seem to leave a leg trailing as Kris Commons went past him and the forward tumbled over it at the edge of the box.

Celtic have been wasteful from the penalty spot of late but Commons' kick was powerful and accurate. Goalkeeper David McGurn had no chance of keeping it out.

James Forrest had not played since aggravating a hamstring injury away to Dundee on Boxing Day but was brought on 30 minutes from time, a bright cameo embroidered by an excellent goal that sealed the win.

His deft touch, as he fastened on to Gary Hooper's pass, showed his time on the sidelines has not blunted his sharpness, while the finish was equally impressive. Assuming the winger feels no ill-effects from his run-out then his comeback will likely continue with an appearance for Scotland against Estonia on Wednesday night. Celtic have managed his return, with their Champions League game in mind, and Forrest would seem on track to face Juventus in eight days.

The third goal was an excellent strike from Charlie Mulgrew as Raith tired. They had provided stoic resistance for most of the match but their endeavours took it out of them and Celtic were able to take advantage. The scoreline was about right given the visitors' dominance, but they found it tough going until their breakthrough on 55 minutes.

Chances until that point had been fairly thin on the ground. Victor Wanyama worked space to thud in a left-foot shot that was saved, then later redirected Adam Matthews' shot straight into the goalkeeper's arms. Mulgrew swung in a corner that evaded everyone to nudge against the far post and dribble away to safety. There was an early penalty appeal, too, when the ball struck Eddie Malone's arm but it was half-hearted and turned down.

Raith had a claim when Joe Ledley eased Jason Thomson to the ground but again there was no real conviction in the appeal. The home side showed marginally more ambition in the second half and finally tested Lukasz Zaluska with a dipping Brian Graham free kick that the goalkeeper pushed away. That sparked a buzz of excitement among the Raith supporters packed in behind the Pole's goal but it would be extinguished just a minute later. Celtic appealed again for a penalty and this one was given, Commons clinical from 12 yards after dusting himself down.

Celtic never looked in any real danger of relinquishing their advantage, although they could have been more comfortable in the closing stages. Substitute Scott Brown made a hash of a good chance when he slashed a shot wide after McGurn had parried Gary Hooper's attempt. It looked easier to score and the home fans were quick to let their fellow Fifer know all about it.

Two goals in the last eight minutes, however, made sure of the win. Forrest was first, finishing well after his sublime touch took him away from Laurie Ellis, before Mulgrew wrapped it up with a swerving shot from outside the box.