Rooney's 58-yard goal spurred United to a 2-0 Premier League victory at Upton Park, and title-chasing Manchester City are next up for Moyes and his men at Old Trafford.
The 28-year-old's eighth-minute opener evoked memories of Beckham's famous halfway-line lob against Wimbledon.
Former England captain Beckham was a conspicuous face in the crowd as Rooney mimicked his long-range effort from that 3-0 Wimbledon victory back on August 17, 1996.
Beckham's wry smile spoke volumes of Rooney's immediate contender for goal of the season, and United manager Moyes suggested the strike can breathe confidence through his revitalised Red Devils.
"It was a great goal by a top, top player: technical ability, and awareness to know exact where the goalkeeper was," said Moyes.
"And to execute and have the power, to drift the ball in the way he did too. My only worry was whether the ball would bounce under the bar or over it.
"I wouldn't comment on whether it's better than Beckham's goal, but more than that I enjoyed his second goal today.
"All the top players get in the right places to score goals and he did that today, for the second.
"We're playing better now, there's a bit more belief, and we have to keep showing that if we can.
"We'll recover and get ourselves ready for Tuesday night, and that belief will be vital."
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