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."
Rooney's goals moved him ahead of Jack Rowley into third on the list of United's all-time top-scorers, with a total of 212 career goals.
Only Denis Law (237) and Bobby Charlton (249) are left for Rooney to eclipse, and the 28-year-old has time and opportunity on his side.
Looking back at his first goal on Saturday, Rooney said on Sky Sports 1: "It's just instinct, I've turned and had a quick look and seen the goalkeeper off his line.
"It's one of those I've tried many times and thankfully today it's gone in. It's up there, I wouldn't say it's my favourite."
Phil Neville was in the starting line-up when Beckham slotted his audacious halfway-line effort at Selhurst Park, and was a spectator for Rooney's similar effort some 18 years later, as part of United's backroom staff.
"Wayne's tried that about 20 times and never managed it, that was the chat from the lads in the dressing room," said Moyes.
"Probably his first goal will maybe take centre-stage, but I thought our performance today was excellent."
Moyes believes United were more impressive at Upton Park than in their 3-0 midweek victory over Olympiacos that saved his side's Champions League bacon.
"Shinji (Kagawa), (Juan) Mata, Rooney, they all stood out," said Moyes.
"Shinji had a great chance, Mata had a great chance, and Marouane Fellaini should have scored from a header.
"Scoring three at West Brom, then three against Olympiakos, and now two today, we're now showing signs of doing it better.
"If anything they stepped up the performance again today."
West Ham had hoped to expose United's defensive injury troubles, with Michael Carrick pressed into emergency centre-half duty.
Andy Carroll was never able to isolate midfield specialist Carrick though, leaving Moyes pleased with the "tag-team" job from Carrick and Fellaini.
"Michael Carrick made the centre-half job look very easy today," Moyes said.
"But I thought he and Marouane Fellaini tag-teamed Andy Carroll today and limited him as much as they could.
"Because we had some problems defensively overall it was an excellent performance."
West Ham manager Sam Allardyce lamented what he saw as a "blatant foul" on defender James Tomkins in the build-up to Rooney's spectacular goal.
Rooney's cheeky nudge in Tomkins' back created the space for his lob.
"It was such a wonderful goal from Wayne Rooney early on but it was a bit of a sickener because I thought it was a blatant foul on James Tomkins," said Allardyce.
"He was easily going to head the ball away. Wayne Rooney took him off his balance when he jumped so he missed the header.
"So technically the referee has made a big error because the opposition have scored from that error."