The Magners League leaders claimed their second Heineken Cup win of the season as they made amends for two previous defeats to the Dragons so far this season.
Having been beaten 30-19 in the Magners League and 22-14 in Europe back in September and October respectively, Glasgow secured a 29-25 victory in their penultimate Heineken Cup group match.
The Warriors crossed for three tries courtesy of Rob Dewy, Johnnie Beattie and Fergus Thomson, with Ruaridh Jackson kicking three penalties and a conversion and Colin Gregor also adding a penalty.
The Dragons hit back with three tries of their own through Rob Sidoli, James Harris and Rhodri Gomer-Davies, while Shaun Connor slotted a penalty and a conversion and Jason Tovey and James Arlidge kicked a conversion and a penalty respectively.
The win for Glasgow sees them leapfrog Gloucester into second place in Pool 2 with an away trip to group leaders Biarritz their final European challenge next weekend.
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