Ayr 1 - 2 Queen of the South: Doonhamers close in on top-four spot
Semple headed home after only four minutes and Dobbie added a second-half penalty before Aaron Muirhead gave Ayr hope with a spot-kick of their own.
United thought they had rescued a point deep in stoppage time through substitute Mark McKenzie but the ball was deemed not to have crossed the line.
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Hide AdQueens boss Allan Johnston admitted: “It became frantic towards the end but the boys are 100 per cent that the ball was not over the line and we also felt it was a dubious penalty against us.
“We are starting to get in touch with the top four and we know we are capable of getting results.”
Mark Kerr, the Ayr player-manager, was forced to take a seat in the stand as a consequence of his red card in last weekend’s 4-0 defeat by leaders Dundee United.
The manager was still making his way to his viewing berth when Ayr should have taken the lead inside 20 seconds.
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Hide AdNew skipper Steven Bell’s ball forward sent Michael Moffat scampering clear in search of his 98th goal as an Honest Man but goalkeeper Robby McCrorie charged off his line to make a fine block.
It was to prove a costly miss as Queens took the lead with their first attack. Darren Lyon forced a corner which was perfectly delivered into the box by Faissal El Bakhtaoui and Semple soared above a static home defence to thunder a free header high into the net.
Home supporters thought they had made the breakthrough when Luke McCowan twice went close, his second effort being headed off the line by Lee Kilday.
Ayr were dealt a hammer blow when Dobbie, set to pull the trigger, was brought down by Muirhead for a penalty. The 37-year-old striker collected himself before wrong-footing Doohan with a textbook spot-kick into the bottom corner.
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Hide AdAyr’s pressure at last paid dividends when Abdul Osman pushed Bell for a penalty, which Muirhead blasted high into the net to prompt concerted pressure including a stoppage-time scramble with Ayr claiming McKenzie’s effort had crossed the line.