After Sunday's battling 24-15 defeat at Northampton, there is no margin for error against the Irish side who have already beaten Gregor Townsend's team in the opening PRO12 fixture of the season at Ravenhill.
Wallace, who skippered Glasgow for six seasons before becoming the club's business development manager, led the team to one of their most famous wins in the tournament when they beat Ulster 30-15 at the old Scotstoun back in 1997.
It was the season when the Warriors came closest to making the knockout stages as they finished behind London Wasps in Pool Two to book a last-eight play-off at Leicester.
Sadly, the trip to Welford Road ended in a club record 90-19 defeat, but Wallace believes a repeat victory over the Ulstermen could be the catalyst to Euro glory this time around.
He said: "That was one of our best displays in Europe back then. Ulster were coming to their best and, of course, went on to win the tournament in 1999 against the French team Colomiers.
"So it was a great victory and I guess there are some parallels with that win back then and Friday night's game.
"This Ulster side are coming off the back of a Heineken Cup final and they are top of the PRO12 and are unbeaten this season in all competitions.
"So we face a similar level of challenge as we did then. But it is one I am confident the boys can meet head-on and deal with."
Wallace added: "We had some great wins at the old Scotstoun and also beat Swansea in the group stages that season. We went on to make the play-offs for the quarter-finals only to take a sore one from a great Leicester side at Welford Road.
"But hopefully the new Scotstoun is on its way to becoming a fortress for Glasgow again and a home win against Ulster would be the perfect start to that and really get our Heineken Cup campaign going."
Wallace realises that Ulster are very much a team on a mission after the tragic death of their young star, Niven Spence.
However, with the men from Ravenhill having already beaten Warriors on the opening day of the PRO12 season, he is confident Glasgow have plenty of motivation of their own.
The former Warriors skipper said: "Because of the terrible tragedy that befell young Niven, Ulster have an emotional driver behind them and, of course, they have already beaten us this season at Ravenhill.
"But I think that is only going to strengthen our motivation to beat them. The bottom line in the Heineken Cup is that you must win your home games and a victory on Friday at Scotstoun is absolutely essential."
Wallace has singled out some of the Ulster dangermen, and said: "Paul Marshall, the scrum-half, is outstanding for them but for me their top player is Ruan Pienaar.
"He has played really well against Glasgow in the past and I think in one game scored all of their points against us. But they have big ball carriers in the likes of Stephen Ferris, and just have a really good depth to them."
Wallace is sure that Ulster will be one of many European teams blown away by the new Scotstoun Stadium and branded it the best arena in Glasgow.
The former Scotland international said: "The change between the old Scotstoun of the Nineties, with its quaint art deco stand, and the new state-of-the-art facility we have now is incredible.
"I would go as far as to say that Scotstoun is the best stadium in Glasgow given all the facilities we have here under one roof."