The Ulstermen could only muster three Paddy Jackson penalties in the narrow 10-9 loss at Ravenhill, their first competitive defeat of the season.
And it could yet get even worse as they could only watch as Bowe, Player of the Championship in the 2010 Six Nations, was stretchered off in the second half with a suspected knee ligament injury.
There was also bad news for Bowe’s Ireland team-mates as defending champions Leinster slipped to a 28-21 defeat to Clermont.
Fly-half Jonny Sexton kicked 11 points to add to tries for fellow Irish internationals Shane Jennings and Fergus McFadden.
But French centre Wesley Fofana crossed in reply and Morgan Parra added seven penalties and a conversion to lift Clermont to the win.
Wales stars Sam Warbuton and Alex Cuthbert also crossed for tries but still ended up on the losing side as Montpellier ran out 34-21 winners against Cardiff Blues.
But there was better news for fly-half Dan Biggar, who is in line to be Wales’ starting Six Nations No. 10 after Rhys Priestland’s injury, as he kicked 12 points as Ospreys beat Toulouse 17-6.
Elsewhere, Exeter recorded back-to-back Heineken Cup victories for the first time in their history as they saw off Scarlets 30-20.
Harlequins thumped Zebre 53-5 while Adam Thompstone’s try proved decisive as Leicester Tigers squeezed past Treviso 14-13.
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