The 15-time major winner had only made the cut with a shot to spare.
Tiger Woods had a third round to forget at the PGA Championship, carding 79 to extinguish any hope of success in Tulsa.
Wales centre Nick Tompkins provided the spark and Theo McFarland the slam dunk as Saracens survived an attack of the first-half jitters to seal a home semi-final.
Rangers lost the Europa League final on penalties before beating Hearts at Hampden Park on Saturday.