Moyes marvels at majestic Rooney strike
The England forward opened the scoring after eight minutes with a looping half-volley from just inside the opposition half, having spotted that West Ham goalkeeper Adrian was off his line.
United were without the injured Robin van Persie, who had scored a hat-trick against Olympiacos on Wednesday to send his side into the UEFA Champions League quarter-finals.
Van Persie's absence was not felt at Upton Park, however, as Rooney followed up his spectacular opener with a second first-half goal after Mark Noble's clearance had fallen into his path.
Moyes was delighted with Rooney's contribution and hailed the 28-year-old's long-range strike.
"It was a great goal by a top, top player," said Moyes. "His technical ability, his awareness to know where the goalkeeper was in the build-up, you'd have never thought he'd be aware of where the goalkeeper is.
"To actually execute it, to have the power and the ability to drift it in the way he did (was fantastic). My only worry was the bounce, was it going to go under the bar or not?
"His second goal was (also important) because he led the line well. He got a bit fortunate, but all the top forwards get fortunate because they get in the right positions and he did that."
Moyes expressed satisfaction with the overall performance of his team and both Shinji Kagawa and Juan Mata also came in for praise.
"The goal (Rooney's first) will take centre stage but I thought our performance was excellent," he added. "Shinji, Juan Mata and Wayne were outstanding.
"The only disappointment is we didn't score more goals from the excellent football we had. Shinji had a great chance, Juan Mata had a really good chance.
"Marouane Fellaini should have scored a header before that as well, so before we scored (the opening goal) we probably should have been ahead."