The Warriors booked a first-ever home semi-final clash at Munster thanks to a 54-0 victory over Zebre on Saturday.
And Grant and co will be hoping home comforts play their part this time around after losing twice in the play-offs at Leinster in the last two RaboDirect PRO12 seasons.
It is Munster this time around and not Leinster standing in their way of the RaboDirect PRO12 final, but Grant is adamant Glasgow can march on to the showpiece.
"We have made history, but that's not enough," said Grant. "We want to win it and we need to win it.
"It's three years we've been building towards this. Everything is in place; it's our task to get the job done.
"It's huge, we've been in the semi-finals twice and it's tough playing away from home, but you can hear the crowd and they've been tremendous for us in the last few weeks.
"We have every chance of making the final. We've had a long history of aggressive battles against Munster and this one will be no different, the boys love it and will look forward to it.
"We knew we had a job to do against Zebre, and what was on the line. All the boys wanted it and we are all playing for our spot next week."
Follow us on Facebook, join the conversation on Twitter, sign up to ourYouTubechannel for extensive match highlights and sign up for ournewsletter for regular updates on the RaboDirect PRO12.
Guinness PRO12
Suite 208, Alexandra House,
The Sweepstakes
Ballsbridge, Dublin 4, Ireland