The England striker, who was 22 on Wednesday, struck the second goal as United finally beat a team which has caused them more problems than most in recent seasons at Old Trafford.
Boro have lost only once on their six previous visits to Old Trafford, but this result was never in doubt after Rooney's strike.
United had enjoyed the perfect start with a dream goal by Nani after only three minutes.
The Portuguese winger collected Owen Hargreaves' pass on the left before leaving Gary O'Neil and Luke Young for dead as he cut in to score with a magnificent 30-yard left-foot shot into the top right-hand corner of the net.
But Boro were behind for only three minutes when slack United defending allowed them back into the game.
Sanli Tuncay turned United defender John O'Shea inside-out on the right-hand side of the United penalty area and his cross into the centre saw the unmarked Jeremie Aliadiere send his glancing header from ten yards into the net off the far post.
United lost their way, although Carlos Tevez and Nani both went close.
But United could have gone behind in the 24th minute when Stewart Downing ghosted in on the blind side of the United defence to head another Tuncay cross inches wide.
It took a terrible defensive error to restore United's lead in the 33rd minute.
Fabio Rochemback's innocuous back-pass to Downing in the Boro box seemed to pose no problems, but the England winger dallied on the ball and had it taken off his toes by Nani.
It fell perfectly for Rooney, charging into the penalty area and he lashed his right-foot shot beyond goalkeeper Mark Schwarzer's hand and into the net from ten yards.
United made it 3-0 ten minutes after the interval. Anderson picked out Tevez 30 yards from the Boro goal and his pass found Rooney inside the box.
The England man produced the cheekiest of back-flicks for Tevez to slot his shot home from 12 yards.
United completed the scoring in the 85th minute when Cristiano Ronaldo sent Rooney racing clear through the middle and he found Tevez on the left side of the Boro penalty area.
Tevez's right-foot shot hit the knees of Boro defender Andrew Taylor with the ball looping up and over Schwarzer's desperate attempt to clear as it bounced into the net.
To add to United's joy, this was their fourth consecutive four-goal scoreline, breaking a century-old record at the club.