Munster boss Declan Kidney claimed his team had "got out of jail" after booking their fourth Heineken Cup final appearance in nine seasons.
The Irish giants, European champions two years ago, now face three-time tournament winners Toulouse at Cardiff's Millennium Stadium on May 24.
But they were pushed to the limit by a mighty display from semi-final opponents Saracens at the Ricoh Arena.
Munster triumphed 18-16 following first-half tries by Ronan O'Gara and Alan Quinlan, while O'Gara kicked two penalties and a conversion, yet Saracens came agonisingly close to knocking them out.
Kidney said: "We got out of jail today, there is no doubt about that. We probably played as well as Saracens allowed us to, and somehow we managed to claw and scrimp our way to the final.
"Saracens were up for it, which we knew they would be. They've beaten the Ospreys and Biarritz in this tournament, and they would have beaten Biarritz in Biarritz during their first pool game except for a last-minute penalty.
"We just stuck in there, really. Things didn't flow for us, and we played an enormous amount of the game in our own half.
"It was one of those games that went with the roll of the dice. Thankfully, it went our way, as sheer guts and work-rate got us through."
After missing out on England's 2015 RBS 6 Nations campaign through injury, centre Brad Barritt admits he is determined to make up for that disappointment in style with club side Saracens during the season run-in.