It was the ideal start to Ulster's Champions Cup campaign as they picked up an opening win, 19-9 over English side Wasps at Kingspan Stadium.
Christian Lealiifano then closed the game out for Les Kiss's men with two late penalties to deny a lacklustre Wasps a losing bonus point as Dai Young's off-form side fell to a fifth straight defeat.
Stockdale wriggled out of a tackle on the left wing before exchanging passes with Piutau. The front five, meanwhile, lined up with Kyle McCall and Wiehahn Herbst either side of hooker Rob Herring, with Kieran Treadwell and skipper Henderson in the second row.
But when Stockdale ripped through the centre of the Wasps defence moments later and the Englishmen infringed again, the scrum-half took advantage of the simplest of kicks to restore parity.
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The teams entered the second period with Wasps leading 6-3 thanks to penalties from Elliot Daly and Jimmy Gopperth, either side of an effort from Ulster's John Cooney.
Yet another lost lineout - this time on their own "22" - drew an infringement from McCloskey and gifted Gopperth another three points seven minutes from the restart.
Then the tide turned.
It was no surprise then in the second half when Ulster scored the only try of the game that both were involved as the Kiwi put the Wasps backline on the back foot before feeding Stockdale who powered over in the corner. Quick hands from Marshall soon got Ulster moving in the right direction, and a close-range penalty to touch brought the best opportunity of the game to date, Lealifano adjudged to have grounded just short of the line by the TMO.
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Bruno Genesio's men, meanwhile, jump up to third in the table after earning their first win in six matches. Prior to the late drama, it looked like as if all the scoring had been done in the first half at Parc OL.
Two minutes later Piutau and Stockdale combined again before McCloskey barged over.
Lealiifano gave Ulster breathing space on 69 minutes with a penalty, Cooney having made way for Paul Marshall.
Great start for Ulster who, face an away trip to La Rochelle in round two.
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