The Dutchman struck twice to give the Old Trafford club their first victory on German soil for 36 years, and allowed him to leap Denis Law in United's European Cup goal-scoring charts.
But it was needlessly tense as the home side took control after the break and narrowly failed to level when Thomas Brdaric headed against a post five minutes from time.
Van Nistelrooy volleyed home his 14th Champions League goal from Juan Sebastian Veron's cross to give the visitors a 31st-minute lead, then tapped in from Nicky Butt's square ball just before the break to give United a handy half-time lead against last year's runners-up.
It should have been a stroll to the finish and a first United win against a German team on opposition soil for 36 years but within six minutes of the restart, Leverkusen had pulled a goal back.
Basturk was the provider, threading a pass through to Berbatov, who had time to arrow his shot into the corner.
Van Nistelrooy spurned a clear shooting chance when he turned Lucio in the home penalty area, instead laying off the ball to Beckham, whose chip drifted just over the top.
Neville laid out John O'Shea when the two clashed heads close to the touchline but after treatment, the Irishman continued.
Butt was yellow-carded for hacking down Bernd Schneider 35 yards out, but while the German international recovered, his illustrious international team-mate Oliver Neuville limped off, replaced after just 22 minutes by Dimitar Berbatov.
Just as the stalemate looked to have set in, up popped van Nistelrooy with the opener.
Veron was the provider, scooping over a right-footed cross from his left wing station. Van Nistelrooy dropped off Balitsch, controlled on his chest, then volleyed into the opposite corner from barely six yards for his fourth Champions League strike of the season.
Brdaric had an immediate chance to equalise but Barthez stopped his volley.
Then, on the intervention of the fourth official Peter Oskam, Rio Ferdinand found himself in the book after clipping Brdaric round the ear.
Neville cleared Berbatov's header off the line, then United scrambled away after Barthez had failed to gather the corner.
The home side were pushing forward with enthusiasm, but a defence which had conceded 12 goals in three goals before last night's encounter was becoming increasingly exposed.
When Giggs found Butt in acres of space inside the area, the England midfielder chose a square ball to the unmarked van Nistelrooy, who bagged his second goal of the game.
United were forced into two changes at the interval.
Gary Neville was brought on for O'Shea, who was suffering double vision as a result of his earlier clash with the younger Neville brother, and Diego Forlan was brought on for van Nistelrooy, who had tweaked a hamstring.
United had disappeared as an attacking force and were suddenly backpedaling.
Barthez was called into action twice to make fine saves from Brdaric and Basturk, but on both occasions, the strikers were ruled off-side anyway.
Balitsch somehow burrowed his way into the area and on the end of Schneider's lofted pass, but he could only hook his shot across goal.
The defender then had to scamper back and halt a Forlan left-wing charge with a smothering rugby tackle, which rightly earned a yellow card.
Slowly, Leverkusen's fire started to dim.
But United couldn't take advantage, Forlan firing into the side-netting on one occasion and poor passes costing another couple of counter-attacking opportunities.
With Solskjaer waiting to be introduced from the bench, Schneider was gifted more space to cross.
He picked out Brdaric perfectly and his flicked header beat Barthez but it came crashing back off the inside of a post.
Veron was the man to make way for Solskjaer.
BAYER LEVERKUSEN: Juric, Zivkovic, Ramelow, Lucio, Balitsch, Babic, Ojigwe, Schneider, Basturk, Brdaric, Neuville.
MAN UTD: Barthez, O'Shea, Ferdinand, Blanc, Silvestre, Beckham, Veron, Phil Neville, Butt, Giggs, van Nistelrooy.