Francesco Minto scored for the Italians in a brave display where they were always up against if from just the sixth minute when Manoa Vosawai was sent off.
The match got off in perfect fashion for Glasgow as they were awarded a penalty right in front of the posts after just four minutes which the superb Ruaridh Jackson gratefully slotted over.
Things went from bad to worse for the visitors however as moments later as flanker Vosawai was shown a red card for a spear tackle on Ali Kellock.
But Treviso responded well with some excellent phases of quick ball but Glasgow were constantly moving the play wide to exploit the extra space in the Italians' defence.
However, it was in the scrum where Glasgow made their presence felt and won their second penalty which Jackson scored on 20 minutes.
And five minutes later the Warriors scored their first try of the game as Hogg passed to Seymour who chipped forward for van der Merwe to pounce on the ball.
The score opened to 20-0 as moments later Hogg was fed by Ryan Wilson and he showed his finishing skills to go over.
But Seymour scored the try of the evening as he plucked the ball from the air to turnover and sprinted 90 yards to go straight under the posts just before half-time.
The second half started scrappily for both teams and Treviso took advantage as lock Minto went over and Kris Burton converted.
The game remained disjointed as Treviso tried to keep the ball moving but were committing too many handling errors to keep their Scottish opponents up against the wall.
But Warriors were also struggling to maintain pressure with the ball in hand and van der Merwe knocked on from a promising position 20 minutes into the second half as they searched for a bonus point.
As the game entered the last ten minutes the bonus point was looking further away than most expected at half-time until Matawalu finally broke through on 74 minutes.
The Fijian evaded his man on the wing to score and looked to have inspired Hogg who grabbed his second of the night moments later to round off an excellent performance which started the year in perfect fashion.
|Glasgow Warriors Score Card|
|DTH van der Merwe||1||5|
|Benetton Treviso Score Card|