The game will see Sean Lineen's team seek to finalise a place in the RaboDirect PRO12 play-offs, yesterday's vital 13-8 win away to Benetton Treviso having kept them in fourth position.
The Warriors still have work to do to be sure of a spot in the semi-finals, their lead over fifth-placed Scarlets currently standing at four points.
A draw against Connacht would guarantee Glasgow a play-off, but the team will be going all out for the win that could see them claim third place.
Munster are in the bronze position at present, with a one-point advantage over the Warriors. The reigning RaboDirect PRO12 champions host Ulster on 5 May, when all the Round 22 games will kick off simultaneously at 7.30pm.
With Leinster and Ospreys having already secured home semi-finals, the Warriors' game against Connacht will be their last ever match at Firhill ahead of the summer move to Scotstoun Stadium.
It will also give the club's supporters the opportunity to salute departing head coach Sean Lineen, defence coach Gary Mercer and a number of players who will take their leave at the end of the season.
Lineed today called on the Warriors fans to help make it the most memorable of nights, telling www.glasgowwarriors.org: "The Connacht game has all the ingredients to be a fantastic occasion for everyone involved with Glasgow Warriors.
"Our supporters have been absolutely magnificent all season, helping us close out some tight battles at Firhill, and we'd love to see the place rocking again on Saturday 5 May.
"Connacht will make it incredibly tough for us to get the result we need, so it would be great to have another big Warriors crowd behind us as we push on for the win.
"Firhill has been a good home for us, and we'll be doing everything we can to give the fans one last terrific memory to take away from the place."
Standalone tickets for the Connacht game are on sale now via www.glasgowwarriors.org, by calling 0844 800 3490 or in person at the Gordon Street and Sauchiehall Street branches of Greaves Sports, our official retail partner.
Supporters who book in advance online or over the phone will receive a £5 discount on the match-day adult price.
We've also put in place a super saver joint ticket covering the crucial Connacht clash and the Saturday of the Emirates Airline Glasgow 7s taking place at Scotstoun Stadium earlier in the day.
Fans can book a £2 one-way bus transfer from Scotstoun and Firhill to take the hassle out of travelling between the two great events.
The joint tickets and bus transfers can be purchased via www.glasgowwarriors.org or by calling 0844 800 3490.
ENDS
Guinness PRO12
Suite 208, Alexandra House,
The Sweepstakes
Ballsbridge, Dublin 4, Ireland