The visitors took the lead after Adam Thompstone scored a brilliant early try but Treviso clawed their way back into the game and took control with 13 unanswered points.
Leicester piled on the pressure in the second half but their efforts were rewarded with just three minutes to go as a series of five-metre scrums proved too much for the hosts to take.
The result, combined with Toulouse's defeat to the Ospreys, leaves the Tigers one point clear at the top of the group with two rounds of fixtures left.
George Ford missed an early penalty in the difficult conditions but other than that attempt it was the home side who showed the greater ambition in the opening stages.
However, Leicester showed a clinical edge to grab a superb breakaway try, with Thompstone rounding off a move which was instigated by Ben Youngs. Ford added the extras.
Treviso No 8 Michele Rizzo was then sent to the sin bin for stamping, but the hosts would not be deterred as, soon after he returned, they tied the scores after being awarded a penalty try.
The decision was somewhat controversial from referee Alain Rolland as the maul was a long way from the line when it was deliberately collapsed, but the hosts needed no second invitation and subsequently took the lead when Alberto Di Bernardo slotted over a penalty.
The score remained 10-7 at half-time but another Di Bernardo penalty shortly after the break extended the lead and left Leicester staring down the barrel of a shock defeat.
The Tigers responded with a period of heavy pressure but could make no further impression on the scoreboard and were still trailing when Treviso centre Christian Loamanu was shown the yellow card in the 67th minute for taking out Geordan Murphy.
Treviso were still holding firm heading into the dying stages but a series of five-metre scrums were driven towards the home try-line before crumpling, prompting Rolland to head under the posts for a second time.
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