That sets up a semi-final with two-time defending champions Toulon in two weeks time while in the meantime focus returns to the GUINNESS PRO12 and a clash with Newport Gwent Dragons.
The men in blue are currently fifth in the domestic table and need a strong run-in in order to make the play-offs this year.
And with two fronts to fight on, Heaslip is desperate for his troops to raise their game as the season approaches the business end.
"We have got to go to another level," said the captain. "That's what we talked about pretty quickly after the game (against Bath).
"A lot of character was shown to stay in the hunt in that last 20 minutes when they had the ball.
"They are a very hard team to defend against and they just kept coming and coming.
"To hold out and not give a penalty away in that last set showed character. We'll take those positives and work on the negatives as well."
Follow us on Facebook, join the conversation on Twitter, sign up to our YouTube channel for extensive match highlights and sign up for our newsletter for regular updates on the GUINNESS PRO12
63x46.png){kind=logo}