Crowley kicked the match-winning drop-goal with Beirne scoring the only Munster try as Healy and Crowley also tacked on penalties.
Munster will face the Stormers in Cape Town on Saturday week in the URC final after an epic semi-final victory over Leinster at the Aviva Stadium on Saturday.
A massive travelling contingent cheered Munster to the victory as Player of the Match Jack Crowley kicked the match-winning drop-goal on 77 minutes to secure a famous victory.
Joe McCarthy’s 62nd-minute try looked to have secured Leinster the victory but Munster attacked brilliantly from their own try-line with two minutes to go and got in position for Craig Casey to pass for Crowley to nervelessly slot over the match-winner.
Tadhg Beirne scored the only Munster try as the Leinster defence stood up superbly throughout but Crowley had the final say to secure a place in the final.