Not least for the contribution of Burton, who playing behind a dominant scrum and lineout, manoeuvred the visitors into the right areas and contributed 18 points including a second-half try.
But they had to survive a ferocious Ulster fightback with Pedrie Wannenburg crossing twice in the final quarter but it could not prevent Brian McLaughlin's side slipping to a third straight defeat.
A bright start for the visitors was rewarded by a penalty after seven minutes by Burton following good pressure in the Ulster 22.
McLaughlin suffered a further blow when summer signing Jared Payne, who was only just back in the team after a spell on the sidelines, had to go off with an ankle injury inside the first 15 minutes.
Burton, who was also in the wars early on, just failed to double their advantage when he pushed a penalty wide following an Ulster offence at the scrum.
The momentum remained with the visitors and having just stopped a Treviso rolling maul inching its way over the line, only a brilliant cover tackle by Darren Cave stopped Brendan Williams touching down after the Australian wing left five Ulster defenders in his wake.
But that merely brought a 5m scrum and, after a succession of collapsed scrums, Ulster's Declan Fitzpatrick was sinbinned for failing to bind properly and the power of tighthead Lorenzo Cittadini eventually forced a penalty try. Burton added the extras for a 10-0 lead.
The hosts had an immediate opportunity to reduce the arrears before the break but Ian Humphreys' radar wasn't tuned in as he hooked his kick wide.
On 50 minutes, Humphries had another opportunity to get Ulster on the scoreboard but he again hooked his kick wide - this time by a far narrower margin.
He was made to pay for his miss as seven minutes later the deadly boot of Burton edged Treviso further ahead after another Ulster infringement.
Burton wasn't done there and he picked off Adam D'Arcy's loose kick to run in from the halfway line before converting his own try.
That left McLaughlin's side needing three converted scores and they immediately fulfilled the first third of that equation with scrum-half Paul Marshall's clever pass allowing Wannenburg to crash over for a converted score.
A famous comeback seemed on the cards as Wannenburg gathered a lineout before smashing his way over but Humphreys' missed conversion left Ulster eight points adrift.
That eased the pressure on Treviso and they were able to control the final stages inside Ulster's 22 and fittingly it was left to Burton to apply the coup de grace with a penalty in front of the posts after another collapsed scrum.
|Ulster Rugby Score Card|
|Benetton Treviso Score Card|