Jaco van der Walt landed a penalty two minutes later to get Edinburgh on the board before Allan restored the seven-point advantage with a kick of his own.
The outside centre attempted a grubber kick through but the ball ricocheted off the boot of Benetton wing Iliesa Ratuva Tavuyara and into the hands of Luke Crosbie for the flanker to crash over and make it 10-10 after 18 minutes.
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Prop Jamie Bhatti was sin-binned for a tackle off the ball in the 34th minute and Benetton instantly took advantage of the numerical advantage with Tomas Baravalle crossing the whitewash.
Allan missed the conversion and van der Walt reduced the arrears to 15-13 with his second penalty with the final kick of the first half.
The torrential rain continued to force mistakes from both sides, with van der Walt converting his third penalty in the 44th minute as Edinburgh got their noses in front.
Allan split the posts 15 minutes later to nudge the Italian outfit back into a lead which would not be overturned, with the Italy international fly-half missing one penalty and opposite number van der Walt dragging two match-winning kicks wide in the final 20 minutes.
– Press Association
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