The England striker scored twice as his side romped to victory in their opening European encounter of the season, with Antonio Valencia and Robin van Persie also on the scoresheet
The England international became only the fourth man in United's history to score 200 goals after notching either side of halftime.
Rooney opened the scoring in the first half with a guided volley but Simon Rolfes equalized against the run of play shortly after the break.
Robin van Persie put United back ahead shortly afterwards, before Rooney pounced on a lapse in the Leverkusen defense to make it 3-1 and Antonio Valencia scored from a superb counterattack.
Omer Toprak pulled one back for Leverkusen with three minutes left - but it was scant consolation.
Marouane Fellaini made his first start for United since his deadline-day move from Everton, while Shinji Kagawa was included in the starting XI for the first time this season.
Similarly, Leverkusen boss Sami Hyypia brought in Giulio Donati, Toprak and Emre Can to bolster the side that defeated Wolfsburg 3-1 on Saturday.
United controlled the tempo in the early exchanges and Chris Smalling almost broke the deadlock in the 22nd minute when he looped a header narrowly over the crossbar.
But just two minutes later the home fans were celebrating a goal their team's play deserved.
Patrice Evra gathered the ball on the left and played a pin-point cross to Rooney, who hit a first-time volley that hit the floor and bounced into the roof of the net – although television replays suggested that Valencia may have blocked goalkeeper Bernd Leno from an offside position.
Moyes' side nearly grabbed a second before halftime when Rooney's 25-yard free kick from the left bounced narrowly wide of Leno's near post before Rooney pounced on a Toprak slip just after the restart but rounded the goalkeeper only to fire wide.
United was immediately punished when Leverkusen made it 1-1 in the 54th minute.
Heung-Min Son held the ball up well in the box before laying back to Rolfes, who hit a first-time bending effort from 20 yards that deflected off Michael Carrick and beyond David De Gea.
They were not level for long, however, as Van Persie restored United's lead in the 59th minute when Valencia surged down the right and centered for the Netherlands international to stretch and guide his volley into the back of the net.
And with 20 minutes remaining, the result was seemingly put beyond doubt when De Gea's long punt down field caused confusion in the Leverkusen defense and Rooney collected on the left before calmly slotting home at the near post. It was a landmark strike from the England man.
Moyes' night got even better when with just 10 minutes left United broke from their own half before Rooney played an accurate ball into the path of Valencia, who rifled home.
With three minutes left, though, Toprak grabbed a consolation when he tapped home a rebounded effort after Stefan Reinartz headed against the crossbar from a corner. But the day belonged to United - and Rooney in particular.