Warriors stand-off Finn Russell weighed in with three penalties and three conversions, prop Gordon Reid scored a try and Mark Bennett was also on the scorecard from the penalty tee as the visitors romped to victory despite a late penalty try for the home side.
Mat Berquist kicked nine points for Treviso with James Ambrosini converting the penalty try in a result which failed to lift them above Zebre and off the bottom of the overall standings, having been leapfrogged by their fellow Italian side following their 30-27 win over Ospreys on Thursday.
Berquist put Treviso ahead in the 13th minute with a penalty, but Russell levelled shortly after before Seymour crossed for his first try of the night in the 21st minute.
Seymour kicked a loose ball from close to the halfway line and gathered to race downfield for the opening try of the game.
Russell converted then traded penalties with Berquist, and Bennett kicked a three-pointer from just inside Glasgow’s half in first-half stoppage time as the visitors took a 19-9 lead into the break.
Seymour scored his second try of the night two minutes after the restart after a lovely pass from Pete Horne, with Russell again adding the extras, then five minutes later loosehead Reid appeared on the wing to cross to take the score to 31-9 in Glasgow’s favour.
The Warriors then lost a man to the sin bin when Tyrone Holmes was shown a yellow card in the 55th minute, but it did not halt Glasgow’s charge as Seymour claimed his hat-trick three minutes later, with Russell again on hand to slot the conversion.
Holmes returned but Glasgow were set to finish the game with 14 men after Rob Harley was shown a yellow card in the 76th minute, with Treviso scoring a late penalty try which was converted by Ambrosini.