Ellis Genge cursed a “missed opportunity” as his Leicester team’s double dream died at Welford Road.
The Premiership leaders had not lost all season at home but their 16-win streak came to an abrupt end against classy Leinster.
The Irish province, coached by former England boss Stuart Lancaster, raced into a 20-0 lead before weathering a second half Tigers fightback to set up a home semi-final with Toulouse.
