It was a victory that denied Leinster a record of its own. A fifth European crown would have seen the Irish side surpass Toulouse and lay claim to being the most successful club side in the northern hemisphere.
But a Billy Vunipola try midway through the second half saw Saracens take control of what was a high quality, bruising encounter.
Saracens’ attention can now turn to the possibility of winning a fourth English Premiership title in five years before the season comes to a close.
“This has been the best achievement of my rugby career so far.
“I’m feeling pretty bruised and battered, but absolutely elated. We’re the best club in Europe and have just won the best competition in club rugby — it’s a pretty good feeling.”
Leinster had raced into a 10-0 lead in the first half thanks to a Johnny Sexton penalty and a Tadhg Furlong try.
A Maro Itoje yellow card handed the defending champions a further advantage, but Saracens rallied, and eventually drew level through a Sean Maitland try on the stroke of halftime.
“My yellow card was all part of the master plan,” Itoje joked after the match. “The team ironically started playing better when I was off the pitch. When things go against us it galvanizes us.
“When we’re against the wall that’s when we truly show our character. We needed to up our physicality and our work rate and the rest is history.
“We’ll celebrate tonight and maybe tomorrow then we’ll see what happens after that.”
Saracens captain Brad Barritt was named man of the match, while Alex Goode was named European Player of the Year, beating Itoje, Owen Farrell, Sean Cronin, Tadhg Furlong and Garry Ringrose to the award.
Fullback Goode has enjoyed a stellar club season but continues to be overlooked by England head coach Eddie Jones, having last represented his country in 2016.
On Friday, Clermont Auvergne defeated French rivals La Rochelle 36-16 to win the Challenge Cup — European rugby’s second tier competition.
Tries from Damian Penaud, Fritz Lee, and Wesley Fofana — as well as 18 points from the boot of Greig Laidlaw — handed Clermont a comfortable victory.