Peter Nelson's first-half try on his first start for the club proved vital with Niall O'Connor adding three penalties but Treviso fly-half Alberto Di Bernardo will have nightmares about his last-gasp penalty that he pulled wide with the Italians on the verge of a famous victory.
Last weekend against Zebre Ulster needed a late penalty try to win and they were somewhat fortunate here as well as the Italians slipped to their fifth consecutive defeat in all competitions despite scoring two tries through Brendan Williams and Ludovico Nitoglia.
Ulster started the brighter of the two sides but only had themselves to blame for falling behind in the eighth minute.
Hooker Rob Herring missed his man at the lineout and Treviso broke quickly through Japanese powerhouse centre Christian Loamanu who went haring clear down the left flank.
His offload found Nitoglia and when he went back inside to full-back Williams the try was inevitable, the pint-sized full-back stepping past the last defender for the first score of the match, Di Bernardo adding the conversion.
Anscombe's men were being a touch careless in possession and despite their territorial dominance it was Treviso who looked the more threatening on the break in the opening stages.
But the Ulster pack soon began to establish themselves in the tight and the loose and in the 18th minute a driving maul from a lineout brought them close to the try-line.
And No.8 Nick Williams thought he had replied for Ulster when he barged over shortly after but TV replays proved inconclusive and they had to settle for an O'Connor penalty instead to reduce their arrears to 7-3.
They did not have to wait much longer for their first try of the match after quick tap penalty from Paul Marshall put Nelson in the clear down the right and the speedster went over for his first-ever Ulster try, O'Connor converting to stretch the lead to three points.
Just before the half-hour mark Treviso were back on level terms however, Di Bernardo slotting a penalty from the halfway line to make it 10-10 after Ulster strayed offside in midfield.
As the interval approached the Italians took the bold decision to kick for touch rather than have Di Bernardo kick for the posts from inside Ulster's half.
And they were rewarded for their bravery when from the subsequent lineout Fabio Semenzato scampered down the blindside and fed Nitoglia who slid over in the left corner to make it 15-10, Di Bernardo this time missing with the conversion.
40 minutes remained for Ulster to rescue their unbeaten start to the season but it was Franco Smith's troops that were on top in the opening stages as Herring and the Ulster lineout continued to misfire.
Anscombe's troops did reduce the lead to only two points in the 49th minute however when O'Connor slotted over his third kick of the night after Treviso went offside.
And the Irish side were really beginning to turn the screw but after a heavy spell of pressure Williams was again denied a try by the TV replays and when O'Connor pulled the subsequent penalty to the left to leave the Italians were still clinging onto their lead.
But the fly-half soon made amends, bisecting the uprights from long range to put the Irish side back in front at 16-15 with the hour mark approaching.
No sooner had they hit the front though than the momentum switched again as the Ulster lineout continued to struggled and Loamanu kept punching holes in their midfield.
And as the game entered the final ten minutes it was Smith's side that looked the more likely winner, Di Bernardo's well-struck penalty from inside his own half drifting just to the right.
A mini-break from Jared Payne relieved the pressure for Ulster but they were fortunate that neither the referee nor the linesman spotted Mike McComish's late high tackle on Di Bernardo.
But a driving maul from the Italians with three minutes remaining took them over halfway and when Ulster conceded a penalty Treviso this time opted to kick for the corner.
Another maul saw the penalty again conceded, well within Di Bernardo's range and slightly to the left but the fly-half could not hold his nerve and dragged his 79th minute effort horribly wide.
Ulster only had 60 seconds to hold out and hold out they did to keep their remarkable streak alive.
|Benetton Treviso Score Card|
|Alberto di Bernardo||1||1||5|
|Ulster Rugby Score Card|