A closely-fought first half saw the Italian side take a narrow advantage at half time, George Ford missing an score-levelling penalty with the last play of the opening 40 minutes.
Leicester had a dominant spell early on, with Adam Thomspstone scoring a try after 12 minutes. Michele Rizzo was sent to the sin bin four minutes later, leaving Treviso a man short.
Alberto di Bernardo added a penalty for Treviso at the start of the second half, before a quiet spell saw few chances for either side.
Tigers had a chance to get back into the match late on when Christian Loamanu was shown a yellow card, reducing Treviso to 14 men.
As the visitors pushed for a try, a Treviso mistake saw Leicester awarded a penalty try, giving Tigers a one-point lead once Ford kicked the conversion.
The win means that Leicester close the gap to Pool 2 leaders Toulouse, who lost to Ospreys, while Treviso are without a win in the Heineken Cup this season.