The Manchester United manager expressed his delight with the Red Devils' improving form after the England striker's two goals inspired a comfortable victory at Upton Park
Rooney lobbed Hammers goalkeeper Adrian from just inside the opposition half in front of former United star David Beckham, who scored from similar distance in 1996 against Wimbledon.
"It was a great goal by a top, top player," Moyes told reporters. "His technical ability, his awareness to know where the goalkeeper was and then to actually execute it, to drift the ball in the way he did, the only worry was whether it would bounce under the bar or not.
"I actually quite enjoyed his second goal! I wouldn't comment on whether it was better than Beckham's or not.
"I thought his second goal, because he was getting in the box and leading the line today, it was a bit fortunate but all the top centre forwards get fortunate because they get in the right place to score goals."
United could have scored more goals during a first half in which they counter-attacked at will, and Moyes expressed his delight with the amount of chances they created in the absence of Robin van Persie.
"The goal will maybe take centre stage but I thought our performance today was very good," he added. Shinji [Kagawa] was excellent, [so was] Juan Mata.
"The disappointment was that we didn't score more from the good football we played. Before we scored we had really threatened and considering we were a bit makeshift defensively there was some really good football."
The 50-year-old was quick, however, to deny the suggestion Rooney could benefit from Van Persie's absence.
"I don't think anyone profits from Robin van Persie's injury," he insisted. "He's a top player and he'll be a massive miss to us in the coming month or so."
West Ham boss Sam Allardyce complained that Rooney had fouled James Tomkins in the build-up to his stunning first goal.
"Such a wonderful goal from Wayne Rooney so early on was a bit of a sickener," he said. "I thought it was a blatant foul on James Tomkins, who was easily going to head the ball away.
"Rooney took him off his balance when he jumped and he missed the header. The referee, in the end, has made a big error as far as I'm concerned because the opposition has scored from that error."