Edinburgh salvaged a late bonus point when Cornell Du Preez went over at the death - Carl Bezuidenhout converting - but there was no time to complete a dramatic comeback.
Alan Solomons' troops may have lost their last two RaboDirect PRO12 away games but had collected two bonus points in doing so with narrow defeats at Scarlets and Connacht.
Meanwhile, Treviso were on an eight-game losing streak in all competitions and found themselves under pressure from the off, with scrum-half Grayson Hart in particular looking menacing.
However, a penalty at scrum time following some cheap Edinburgh turnovers saw the hosts assume the front foot, Tobias Botes knocking over the first penalty of the match.
A ten-minute spell of Treviso pressure immediately followed but eventually, the visitors managed to wriggle free from their own 22 and started to assert their own authority.
The Italians were pinged in the ruck and Bezuidenhout took the opportunity to get Edinburgh off the mark with a three-pointer of his own.
Soon after the South African pulled a long-range penalty wide but chances continued to land in his lap after aggressive rucking by Ross Ford and David Denton forced Treviso into another mistake.
Bezuidenhout stroked the penalty through to edge Edinburgh into the lead and it wasn't just with the boot through which the full-back was making an impact, breaking through the lines - only to pop off a forward pass.
And they could have ended the half with the game's first try but Du Preez decided to go it alone in a three-on-two situation.
However, the play was pulled back for a penalty and Bezuidenhout made no mistake as Edinburgh headed into the break with a six-point advantage.
Edinburgh hands in a ruck allowed Treviso to get straight back into the match when the two teams returned as Botes made no mistake with the penalty.
And the momentum was well and truly swinging the home side's way after Lorenzo Cittadini wrestled his way to the whitewash under the close attention of Andries Strauss.
The TMO was called and on replay, Strauss had ripped the ball away from Cittadini's grasp at the last second.
Treviso however were undeterred and found a richly-deserved breakthrough after hooker Ghiraldini waltzed through Edinburgh lines for the score.
It did not take long for them to press home their advantage either with another stroke of front-row magic, Italian international de Marchi burrowing over to make it two tries in four minutes.
Botes converted and Treviso kept Edinburgh at bay until the clock went red and while Du Preez sealed another losing bonus point for his side, the hosts breathed a major sigh of relief.
|Benetton Treviso Score Card|
|Alberto de Marchi||1||5|
|Edinburgh Rugby Score Card|
|Cornell du Preez||1||5|