Once again sporting a black headband to protect a facial injury he picked up last month, Rooney scored twice and made another goal as Moyes made a memorable European bow at Old Trafford.
Overseeing his first continental game since succeeding Alex Ferguson as manager, Moyes saw Rooney, his former Everton protege, give United a 22nd-minute lead.
Simon Rolfes equalised with a deflected shot in the 54th minute, but Robin van Persie's fine volley restored United's advantage five minutes later and further goals from Rooney and Antonio Valencia completed the job.
United fought to keep Rooney out of Chelsea's clutches during the close-season, but when asked if he had asked to leave the club, he would only repeat: "I'm concentrating on my football."
He added: "I am really pleased to score 200 goals for a club like Manchester United. It is a great honour."
After an uncertain start to the season, United appear to have rediscovered their scoring touch ahead of Sunday's trip to derby rivals Manchester City in the Premier League. "It was a good job tonight," Moyes told ITV.
"I said several months ago Wayne Rooney could join the real greats with his goal-scoring. He could have got a hat-trick tonight."
Leverkusen coach Sami Hyypia, another Champions League novice, saw Omer Toprak add a late goal, but it was a chastening evening for the Finn, whose side must also contend with Shakhtar Donetsk and Real Sociedad in Group A. The Ukrainians won 1-0 in San Sebastian.
"Today we lost to a better team," said the former Liverpool defender. "We might have shown them too much respect, we were perhaps a bit nervous, and we didn't press them enough."
United made the breakthrough midway through the first half, Rooney dispatching a cross from Patrice Evra with a side-foot volley, but Leverkusen appeared to have twofold grounds for complaint.
Evra looked marginally offside as he crossed from the left and Valencia, backing into Leverkusen goalkeeper Bernd Leno, was clearly offside and seemed to be interfering with play when the ball left Rooney's foot.
Nonetheless, the goal stood and Rooney went close to adding to it with a replica of his free-kick from Saturday's 2-0 win over Crystal Palace, only to bend his shot a foot too far.
It should have been 2-0 early in the second half but Rooney let the German side off the hook when a goal seemed certain.
After seizing on a slip by Toprak, the United number 10 rounded Leno but, with the goal vacant and Van Persie charging in, he somehow contrived to miss both net and team-mate with a low cross-shot.
Moments later Leverkusen equalised, Rolfes curling a shot inside the left-hand post via a deflection off Michael Carrick, but although Moyes put his head in his hands, his side took just five minutes to respond.
Valencia motored into space on the right before dispatching a cross and Van Persie showed wonderful agility to meet the ball with a hip-high right-foot volley that a startled Leno could not keep out.
The hosts' failure to clear in the 69th minute allowed substitute Lars Bender a crack at goal, but David De Gea saved smartly and, from the United goalkeeper's resulting kick, Rooney doubled his side's lead.
Emir Spahic could only head the ball into Rooney's path and the England striker shortened his stride before whipping the ball past Leno at his near post to bring up a double-century of United goals.
Rooney completed his night's work by teeing up Valencia to drill home United's fourth in the 79th minute.
A calamitous finale saw Toprak pull a goal back with two minutes to play after De Gea flapped at a corner before Van Persie somehow missed an open goal from two yards out, but it was not enough to spoil Moyes's night.