The Dutchman's 27th-minute strike deflected off Phil Bardsley and Titus Bramble en route past Simon Mignolet, but van Persie has no doubt that his seven-game goalless run is over.
"Of course, no question about that," he told Sky Sports. "I think you could see (I enjoyed it). It's been a while so it was good to score again, and it was an important goal. Today it was all about three points and we got them.
"We knew before that it was going to be tough; away at Sunderland is always going to be very hard. They work hard and play a game with lots of long balls, second balls and we had to dig in. We did that, everyone fought hard for a deserved win."
Sunderland were restricted to few clear openings - David De Gea made his first save in the 90th minute - and van Persie felt that the outcome was never in doubt, despite United's slender lead.
"This team, if you ask me, is just full of winners," he said. "Everyone knows what he has to do. I was never in doubt, even if it was still a small score at 1-0.
"I was always confident we would win this game because of players like Mike (Carrick), Vida (Nemanja Vidic), Chris (Smalling) has been playing really well, Alex (Büttner) just comes in and plays well... everyone knows what he has to do and we did it again."
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