Man of the match Beck led the rout against the outclassed Italians as the home side raced over for six tries to pick up their first try bonus point of the season in all competitions.
The Welsh region must now hope Pool 5 leaders Saracens don’t beat Biarritz Olympique on Sunday to remain in the mix for Heineken Cup and Amlin Challenge Cup quarter-final places moving into the final round next weekend.
Tommy Bowe started proceedings with a third minute interception try from 60 metres out before the Ospreys stretched their lead to 10-3 with a Dan Biggar penalty.
Edoardo Gori outpaced Bowe by racing 80 metres to the left corner for a spectacular try. Kris Burton’s excellent sideline conversion made it 10-10 in only the 11th minute.
But Beck’s two touchdowns before the break gave his side a handy 25-10 interval lead and once the Ospreys pack went into overdrive to claim two penalty tries, there was no way back for the Italians.
But Treviso refused to be shaken off and a try from close range by lock Gonzalo Padro, improved by Tobie Botes, cut the gap. Repalcement scrum half Khan Fotualili also crossed for the victors.
