The Warriors lived up to their name with an historic win away to Leinster last weekend but back on home soil it was a case of after the Lord Mayor's Show as the Italians were well worth their victory - leaving Sean Lineen's men having to settle for a losing bonus point.
Glasgow began brightly enough and fly-half Duncan Weir opened the scoring with a fine try, finishing off lock Tom Ryder's break before adding the extras on 11 minutes.
But Treviso hit straight back and got their just desserts on 17 minutes. Burton, having already missed one penalty, made no mistake with his second to cut the deficit to four.
The match arguably slipped away from the Warriors in the second quarter of the match when Weir missed two penalties before Warriors hooker Pat MacArthur was sent to the bin on 25 minutes.
Burton added two penalties before half-time to give the visitors a 9-7 lead at the break although they would have been disappointed not have come away with a try having hammered hard at the Warriors' line.
Soon after the break however, the lead swung again with Treviso captain Antonio Pavanello shown a yellow card and Weir capitalised with his first penalty of the night to edge the hosts ahead by a point.
Burton swiftly responded and after Weir was off target, Warriors boss Sean Lineen opted to introduce Wight and with 13 minutes to go the replacement was on target for the hosts.
But their lead was shortlived as Burton dropped back into the pocket to give the visitors a narrow advantage.
Wight was presented with a relatively simple opportunity to make himself a hero with another penalty with two minutes remaining but he was off target, handing Treviso a historic win.
|Glasgow Warriors Score Card|
|Benetton Treviso Score Card|