Having secured a bonus point in defeat away to Munster last Saturday, Sean Lineen's team currently occupy fourth spot in the RaboDirect PRO12, but know that Ulster and Scarlets are right on their tails as the battle for semi-final spots reaches a climax.
Glasgow have lost only two of their last 16 games in the tournament, and emerged victorious from their last venture to Italian soil, an 18-6 victory against Aironi last November.
However, they make the trip fully aware of the threat posed by Treviso, who were the last team to beat them at Firhill in the RaboDirect PRO12. The men from the Veneto claimed a 15-13 win there last September, and recorded a thrilling 33-32 success away to Dragons last week.
The Warriors team for Sunday's game will be confirmed tomorrow, with Lineen buoyed by the news that centre Graeme Morrison (pictured) and back-rower John Barclay are back in the selection mix having shown good progress in their recoveries from the respective knee and head knocks they sustained against Cardiff Blues on 30 March.
Scrum-half Chris Cusiter, meanwhile, will be subject to further assessment on the blow to the head he suffered in the Munster game.
Lineen told www.glasgowwarriors.org: "For a while now, the next game has been our biggest of the season, and that's certainly the case again this weekend.
"We know we have to win this match if we're going to make the play-offs, and there's absolute clarity and focus among the players about what we need to achieve and how we're going to do it.
"Treviso is right up there with the toughest places you can go in the RaboDirect PRO12. They're a passionate team with supporters to match, and some of the results they've recorded this season speak for themselves.
"The wins we've managed on the road this season at places like Leinster, Cardiff, Ospreys and Aironi have been brought about by 23 players performing right at the top of their game. That's the recipe again this weekend, and we're certainly going to have to be much better collectively than was the case in Munster.
"We didn't get into that game anywhere near quickly enough, and we paid for it in the tries and penalties we conceded. The second half performance was much more like the real Glasgow Warriors, but we still need to see an improvement in terms of discipline and composure.
"We've seen a good number of times this season that the players know what it takes to deliver when the pressure is on, and we've every confidence they will back up all that good work with another winning performance come Sunday.
"It's good to have Graeme and John back available for selection. They're two massively experienced players who know all about the dynamics of the big occasion, and that sort of insight is invaluable in the context of the relatively young side we've got."
The Warriors are assured of some vocal support in the Stadio di Monigo, with a 35-strong group from Greenock Wanderers heading to Italy.
The Fort Matilda crew are playing local side Paese RFC (based only 5km away from Treviso) on Saturday evening, before heading to the Glasgow match on the Sunday.
The Warriors have provided the group with an allocation of complimentary tickets as a thank you for their support.
Fans unable to make the trip are invited to a special screening of BBC ALBA's live coverage at Waxy O'Connor's, 44 George Street, Glasgow.
Warriors players will be in attendance to take in the action with supporters, with the match being shown in the Guinness and Church areas on the basement level of the city centre bar.
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