Robbie Keane's second half hat-trick saw Celtic beat Kilmarnock 3-0 in their Active Nation Scottish Cup quarter-final clash at Rugby Park.
The home side had the best of the first half with Allan Russell clipping the bar with a shot.
However, the tide turned in the 63rd minute when the Republic of Ireland striker opened the scoring from Edson Braafheid's long ball and a brace within a minute later on secured the visitors a place in Monday's semi-final draw.
Kilmarnock slowly grew in confidence and Russell got the break of the ball in the 14th minute after captain Craig Bryson had driven at the Parkhead defence and his curled shot from 16 yards beat goalkeeper Lukasz Zaluska but clipped the top of the bar.
At the other end a Braafheid free-kick from 25 yards was held by Kilmarnock goalkeeper Cameron Bell, who made an even better save when he blocked Keane's close-range shot after he had been threaded in by Marc Crosas.
The visitors, apparently rejuvenated by Mowbray's half-time pep-talk, almost broke the deadlock two minutes after the restart. Killie failed to clear their lines from a Celtic attack, allowing the foraging Keane to chip the ball up for a Aiden McGeady volley which was speeding past Bell and towards the top corner until Frazer Wright bravely headed clear.
In the 55th minute Russell again hit the woodwork when Tim Clancy's cross from the left was flicked on by Mark Burchill. As the Parkhead defence hesitated Russell stole in at the near post but Zaluska did enough to prevent the Killie striker getting a clean shot away and the ball hit the post before bouncing wide.
But in the 63rd minute it was Keane who gave Celtic the lead and it came courtesy of a long and hopeful ball from Braafheid. The pass caught the Kilmarnock defence sleeping and Keane's first touch took the ball past Bell and he calmly stroked the ball into the empty net.
And, the tie was all over in the 81st minute when Georgios Samaras robbed the hesitant Wright on the touchline and played in Marc-Antoine Fortune who rolled the ball past Bell for Keane to tap into an empty net.
A minute later Fortune set up Keane again and this time the Hoops' striker almost casually rattled a drive past Bell to take collection of the match ball.
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