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Rangers earned a place in the Scottish Cup fourth round with a narrow win over fellow Championship side Dumbarton.

Kris Boyd was the match-winner with a strike in first-half injury time.

Rangers dominated the second half but could not find a second goal to kill the tie despite a number of efforts.

The closest Dumbarton came to a goal was an Andrew Graham header, which Lee Robinson got down well to save. His only other serious involvement was to block an early Mitch Megginson drive.

Indeed neither side was able to trouble the opposition keeper in the first 45 minutes to any great degree, although Boyd did have the ball in the net from a Richard Foster cross, only for the offside flag to cut short his celebrations.

But that did not last long as it was only a minute before he latched onto Lewis Macleod's threaded pass to score off the inside of the post.

While that may have been cruel on the home side after an even first half, the visitors controlled the second period and Boyd should have had a second when sent clear on goal, but the legs of Dumbarton keeper Jamie Ewings denied him.

Kenny Miller, Macleod and Ian Black all had decent efforts but were unable to add to the lead.

But Graham's header and a last-gasp free kick from Scott Agnew that flew over the bar was all Dumbarton could muster as they searched in vain for an equaliser.