Heading into the game, Edinburgh had managed just three wins in nine GUINNESS PRO12 matches this season, losing their last encounter, to Italian side Zebre, 18-10 last month.
Their European form however has been in stark contrast, continuing their unbeaten run in the competition with back-to-back wins over London Welsh in recent weeks.
And with attention switching back to domestic matters at BT Murrayfield on Friday night, it appeared the Scottish outfit had maintained that momentum.
Sam Hidalgo-Clyne, Mike Coman, WP Nel, Grayson Hart, Dave Denton and Grant all went over in the bonus-point win while Hidalgo-Clyne also contributed 12 points from the tee, alongside three conversions for Tom Heathcote.
And while pleased with the scoreline, Grant insists there are still things to work on to ensure an 80-minute performance.
"It is always good to win by 48 points and to nil a team. We are still frustrated as we didn't play a great game for 80 minutes but we are really pleased with the score," said Grant.
"In Europe we've done well in but the PRO12 we haven't had the results we've wanted and we need points to climb that table. We really needed to build on our performances and we are starting to do that.
"It was good to play better but it wasn't the complete performance. Our thoughts already are with Glasgow in our next game.
"Treviso are a very physical side and that was the key coming into this game, they have a big pack and are physical and we needed to front up to that and we did that and subsequently won the game."
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