Rooney tormented Leverkusen with pinpoint passes, having a hand in four goals in all, in what was United's biggest away victory in the European Cup in over half a century since a 6-0 demolition of Shamrock Rovers in 1957. (Agencies)
He found Antonio Valencia with a deep cross for an easy tap-in before floating a free kick into the box which defender Emir Spahic headed into his own net in the 30th minute.
Jonny Evans added another after taking advantage of some confusion in the box and Chris Smalling scored in the 77th before a cute Nani finish made sure of English clubs' fifth win in seven matches against German teams this season.
"This is probably the best performance of the season, the best we played in my time here," said United coach David Moyes, whose domestic results have been mixed since succeeding Alex Ferguson in the close season.
"For us to come away from home and score five goals is special,” he said.
"Wayne was very good tonight. There were so many great performances. That is what I was hoping to get more often this season. There are signs that we have been getting better."
The win lifted United, who were playing without injured Nemanja Vidic and Robin van Persie, to 11 points in Group A, three ahead of Ukraine's Shakhtar Donetsk, with Leverkusen in third on seven.
A win or draw against the Ukrainians at home in the final group game on Dec. 10 will guarantee the English team top spot.
"We really killed them on the counter-attack and it was a pleasure to play behind the front four," midfielder Ryan Giggs, who will turn 40 in two days, told Sky Sports.
Improving United, with former manager Ferguson in the stands, were out to protect a 10-match unbeaten streak in all competitions and took some time to find their footing with Nani curling a first effort narrowly over the bar after 15 minutes.
Unmarked Valencia did it better in the 22nd, connecting perfectly with a smooth Rooney cross after a quick break launched by Shinji Kagawa to give United the lead.
Leverkusen, missing the pace of injured winger Sidney Sam, briefly jumped into action and Stefan Kiessling came close for the hosts only to be denied at the last moment by Evans.
With Leverkusen searching for the equaliser, Rooney set up United's second goal, floating a dangerous free kick into the box and Spahic rising above everyone to head in an own goal.
The hapless hosts, second in the Bundesliga, battled to come back and Stefan Reinartz hit the post with a header on the hour but United remained a constant threat with England striker Rooney coming close with a long-range effort.
Evans added a third goal in the 66th with Leverkusen's defence failing to clear the ball after a Rooney stab was saved by keeper Bernd Leno.
Rooney then set up Chris Smalling with a clever chip and Nani finished with aplomb.
Leverkusen are now hoping to beat eliminated Real Sociedad in Spain while United defeat Shakhtar.
Rooney tormented Leverkusen with pinpoint passes, having a hand in four goals in all, in what was United's biggest away victory in the European Cup in over half a century since a 6-0 demolition of Shamrock Rovers in 1957.