The star-studded squad Sarries has assembled will be hit by departures at the end of the campaign after the club was administratively relegated from the Premiership for salary cap breaches.
However, the holders appear determined to go out on a high in European competition and a dominant first half was enough for them to defeat the Pro14 champion 25-17.
Sarries led 22-3 at half-time, Alex Goode kicking three penalties and converting his own try while Elliot Daly added another pair of three-pointers.
Andrew Porter and Jordan Larmour crossed for Leinster in the second half to narrow the gap to five points, but Saracens held on and Goode's late penalty clinched victory.
Captain Brad Barritt, who will leave the club at the end of the season, said: "It was the prospect of having another week together.
"We know after this season there will be a slightly different-looking squad and we owed it to ourselves to have a big game. We showed a huge amount of character playing in games that don't mean anything.
"Today was about fighting for something tangible. We owed it to ourselves to represent the Saracens badge and I couldn't be more proud of my team."
Sunday's (AEST) other quarter-final saw Racing 92 claim victory over Top 14 rival Clermont Auvergne.
Racing led 24-8 at half-time, with six penalties from Teddy Iribaren and tries from Louis Dupichot and Francois Trinh-Duc key to the 36-27 success despite a spirited second-half showing from Clermont.