The joint-leading try scorer from the pool stages with six, Stockdale, pictured, crucially lost control of the ball past the try-line early in the second half, and despite Luke Marshall’s subsequent try bringing them level, the Ulstermen fell short thanks to Ross Byrne’s 71st-minute penalty after a dominant final 41 phases of possession rugby from the hosts.
A surprise result looked a possibility when Kieran Treadwell and Byrne, who deputised at fly-half for the injured Jonathan Sexton, swapped tries inside the opening 10 minutes.
Despite losing captain Rory Best to an early ankle injury, John Cooney’s eight points from the tee had Dan McFarland’s Ulster underdogs 13-11 ahead at half-time.
It was a tale of two wingers when Stockdale agonisingly dropped the ball from his grasp, and a subsequent Leinster attack sent Adam Byrne over for a momentum-shifting 53rd-minute score.
The home side and Champions Cup holders had to show huge resilience in the end, coming through the setback of Dan Leavy’s horrific knee injury and Marshall’s levelling five-pointer to settle the issue through Byrne’s reliable right boot.