A goal in each half from Cillian Sheridan and Borja Perez was enough to see Kilmarnock into the next round of the William Hill Scottish Cup.
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The plucky visitors, who played 88 minutes with 10 men after Stevie McKenna saw red, made them fight all the way, especially in the closing stages after Nicky Clark pulled a goal back with 13 minutes remaining.
Boasting the only unbeaten league record in Scotland, the Second Division side started the game full of confidence.
However, their prospects were dealt a severe blow within 90 seconds when, for the second consecutive week the Rugby Park fans witnessed a controversial red card for a two footed challenge.
In what was the first tackle of the game, the
McKenna went in high on Borja Perez and referee Mike Tumilty brandished a red card much to the amazement of both sets of fans.
It nearly got worse for the Dumfries side two minutes later when Lee Robinson had to produce a great double save to keep out the home side.
Paul Heffernan's touch had the keeper at full stretch to palm the ball out, but with Robinson grounded Ryan O'Leary should have done better as his shot was blocked by the keeper's legs.
The Queen's keeper was helpless, though, after eight minutes when Killie grabbed the opener. A floating corner from Perez found Sheridan unmarked at the back of the six yard box and his shot found the back of the net.
A man and goal down the Palmerston side took time to settle and in the 19th minute got the their first chance after Nicky Clark was tripped at the edge of the box. Chris Mitchell drilled the free kick towards goal and a deflection had Cammy Bell diving to smother the ball.
The Second Division side continued to grow in confidence and after 34 minutes Ryan McGuffie collected the ball 16 yards out but weakly pulled his shot wide of goal.
In the final minute of the first half Kilmarnock came within inches of increasing their lead when a thundering shot from Gary Harkins
rebounded from the face of the cross bar and as the ball was returned across the six yard box Sheridan failed to direct the ball towards an open goal.
Then in injury time it was the visitor's turn to come within inches of an equaliser. Paul Burns squared the ball to Clark eight yards out and although he squeezed the ball past Bell it passed narrowly on the wrong side of the post.
The home side
started the second half in determined mood and a cross from Danny Racchi found Sheridan whose glancing header bounced just wide.
The Killie marksman came even closer to a second goal after 55 minutes. Perez was again the provider feeding the ball to the edge of the box and Sheridan's terrific volley dipped past the keeper only to rebound from the cross bar.
The visitors remained confident in possession and when Derek Lyle found himself unmarked in the six yard box his powerful drive was brilliantly pushed away by Bell.
Then in the 67 minute a great cross from McGuffie sparked off a goalmouth melee. Calmly, though, Jeroen Tesselaar carried the ball out of the danger area to set up a speedy attack. And when Harkins cut the ball back in front of goal Perez stroked the ball into the corner of the net to make it 2-0.
That should have killed the tie but with 13 minutes left Queen's deservedly reduced the leeway.
Another teasing cross from McGuffie found Clark just outside the six yard box and his diving header sent the ball high beyond Bell and into the roof of the net to make it a tense finish.