Omer Toprak poked in a close-range consolation in the 88th for Leverkusen, which failed to reproduce the form it has shown so far in the Bundesliga where the team has won four matches out of five.
Leverkusen hadn't come up against such a potent combination as Rooney and Van Persie, though.
"It looks so easy the way he is playing," Leverkusen coach Sami Hyypia said of Rooney. "He is still scoring goals and he will continue to score them."
Moyes was taking charge of his first group-stage match in the Champions League and saw his team hit the ground running in its record 18th straight season in Europe's top competition, producing a performance that was much improved from its underwhelming start to the Premier League.
The margin of victory should have been even larger, with Rooney and Van Persie both missing open goals. Van Persie's effort was particularly remarkable, sidefooting wide from barely a yard out.
Rooney can still look back with much fondness on an evening when he reached another scoring milestone for United. Only three other players Bobby Charlton (249), Denis Law (237) and Jack Rowley (211) have scored more than 200 goals for the club and Rooney is still only 27.
Wearing a thick headband to cover a deep gash to his forehead sustained in training 2 weeks ago, the England striker looked sharp and full of running in the hole behind Van Persie, underlining just why United fought so hard to keep him this summer.
"If we are going to win the Champions League, we need to have several world-class players and Wayne comes into that category," Moyes said. "I remember coming here and saying he has the chance to become one of the all-time leading goal scorers at this club. If he keeps playing like he did tonight, he'll get there."
Rooney and Van Persie were also both on target in a 2-0 win over Crystal Palace in the league on Saturday, and it is a partnership that Moyes is clearly banking on in his first season at United.
The opener Rooney's 199th in all competitions for United had a hint of fortune about it, though. Patrice Evra was just offside when he swung a cross in to Rooney and Valencia was also offside and hindering goalkeeper Bernd Leno as the striker volleyed downward and into the net.
United fully deserved its halftime lead, though, against an initially compact Leverkusen side whose defense was ripped apart after the break.
Rooney will be glad his glaring 52nd-minute miss didn't come back to haunt him and United. Toprak slipped to allow the striker to run through on goal but after rounding Leno, Rooney was caught between shooting into an unguarded net and crossing for the unmarked Van Persie. What ended up being a cross-cum-shot agonizingly rolled just wide of the far post.
Rolfes made him pay two minutes later by bending in a shot from the edge of the area with Leverkusen's first real chance, but the lead was restored in the 59th.
Valencia raced to the byline and crossed for Van Persie to send a flying volley toward Leno, who could only bat the ball into his own net.
Rooney then pounced on Toprak's poor headed clearance to beat Leno at his near post in the 70th, before slipping a ball through to Valencia following a quick counterattack for the winger to fizz a low shot in at the near post.
"Obviously the first game in the Champions League is always important and thankfully we got the victory," Rooney said.
