Dan Biggar had a torrid night from the tee in windy conditions and while the Ospreys had plenty of possession they squandered their second-half chances.
The Ospreys began the defence of their title in menacing fashion but Treviso's defensive line refused to be breached early on and it was the hosts who opened the scoring, Kris Burton on target with a seventh-minute penalty.
Evans' first yellow card came just two minutes later and knocked the wind out of the Ospreys' sails - the Wales second row sin-binned for a deliberate indiscretion on the floor.
It was typical of the Ospreys' indiscipline in the first half with the visitors conceding four penalties within the first 14 minutes with Burton able to convert two to give Treviso a 9-0 lead.
Ospreys regrouped and were able to get themselves on the scoresheet on 18 minutes as Biggar kicked his first points of the night on 18 minutes but that did not knock Treviso out of their stride - even if Burton did endure his first miss of the night on 24 minutes.
Then came the major turning point of the match on half an hour as Evans was shown a second yellow card for a high tackle and Italy international Burton rubbed salt into the wounds, taking his and Treviso's tally to 12.
The Ospreys were shaken but they came out fighting and forced another penalty of their own, only for Biggar to miss the target, handing Treviso a 12-3 lead at the half-time interval.
Despite their numerical disadvantage, the Ospreys weren't going to go quietly into the night and they came out for the second half with fire in their bellies and earned themselves a 44th-minute penalty - only for Biggar's uncharacteristic waywardness to continue.
The field of play was temporarily levelled just a minute later however as prop Ignacio Fernandez-Rouyet was sent to the bin for a dangerous tackle and this time Biggar made no mistake to trim Treviso's lead to six.
But his indifferent night continued on 50 minutes as he failed to release to Hanno Dirksen early enough on the left wing when the South African-born flyer was well placed.
The Ospreys' onslaught continued and on 53 minutes Ashley Beck looked certain to score but he was excellently held up at the last by Treviso centre Tommaso Iannone.
Treviso soon found themselves down to 14 again when flanker Dean Budd was also shown yellow for a dangerous tackle but again Biggar struggled with the wind and dragged his effort wide.
The Ospreys kept coming but could not produce the goods when it mattered and on 68 minutes, Tom Isaacs was the culprit, failing to collect a pass after a flowing move in the left corner.
And while the Ospreys dominated possession in the closing stages they failed to find the cutting edge they had searched for all night - Rhys Webb fumbling when well placed late on - ensuring Treviso begin their season with a bang.
|Benetton Treviso Score Card|
|Ospreys Score Card|