Shortly after Kovalchuk banged a power-play shot off the post, Del Zotto swatted a shoulder-high pass from the corner by Derek Stepan into the net at 11:49 for New York's third short-handed goal of the season.
Centre Jamie was the architect as he intercepted an Edinburgh pass in the visitors' 22 and fly-half Nicky was on his shoulder to take the pass and race under the posts.
Laulala fed Rush and then followed the back-row on the inside shoulder, picking a pass off his shins for a deserved try that went unconverted - although Parks' kick was genuinely tricky close to the right touchline.
Reo-Coker was then let down by Ashley Young's inability to bring the ball under control after he had pushed a smart pass through with the England winger lurking on the shoulder of Sunderland's defenders.