Defences had taken control in the opening half as the teams went in scoreless at the break, although Zebre will have been the happier of the two having seen both props, Salvatore Perugini and Carlo Fazzari sent to the sin bin.
However it was in the absence of Fazzari, early in the second half, that Treviso managed the decisive score, with Di Bernardo knocking over the conversion to make it 7-0.
On the hour-mark Zebre hit back with a penalty from Luciano Orquera, but the Italy fly-half missed his second attempt six minutes later.
And with four minutes remaining Di Bernardo slotted his first penalty of the afternoon to seal the win ahead of next week's return fixture in Treviso.
Treviso had made the quicker start when Dries Van Schalkwyk was penalised for offside after just three minutes but Di Bernardo's penalty drifted wide.
The visitors were dominating both at the set-piece and in terms of possession, and eventually Perugini was given a yellow card when he was caught offside.
Two minutes earlier Di Bernardo had missed a penalty attempt from a powerful Treviso scrum and he was again off-target on 20 minutes as his third effort bounced back off the post.
The Zebre scrum was still under massive pressure, and it was no surprise that Fazzari was also given a ten-minute break.
Treviso made much the quicker start to the second half and after a period of pressure on the Zebre line, it was the power of Loamanu which saw the visitors open the scoring.
The Japanese international racked up his third try of the season, with Di Bernardo finally hitting the target with the conversion.
Di Bernardo missed another shot at goal soon after, and when Orquera took advantage of Zebre's first chance of the day it looked like they might mount a comeback.
But despite a few threatening attacks, Treviso hung on, and even added another penalty through Di Bernardo.
|Zebre Score Card|
|Benetton Treviso Score Card|
|Alberto di Bernardo||1||1||5|