United controlled the game and Boro finished the 90 minutes without managing a single shot on target.
Boro failed to cope with United's pace and running power. Indeed, it was remarkable that the visitors failed to score their second goal until the closing minutes.
It was a stroll by in-form United against a very disappointing Middlesbrough side.
United took an early lead through Darren Fletcher and the issue was never in doubt after the goal. The movement of United in the first half, in particular, was tremendous.
Boro manager Steve McClaren, the former number two at Old Trafford, must have been bitterly disappointed with the performance of his side.
The defence never inspired confidence and there is no question the midfield is lacking the ability and aggression of the injured George Boateng.
United boss Sir Alex Ferguson has refused to give up the fight for Premier League honours. Chelsea have a commanding lead at the top of the table, and are strong favourites for the title, but United will keep pegging away, hoping their London rivals slip up.
The game marked the 600th League appearance of veteran Middlesbrough defender Colin Cooper, a remarkable record for a north-east born player who has graced the game for 20 years.
The hosts opened promisingly with local hero Stewart Downing firing over a left-wing cross that Jimmy Floyd Hasselbaink just failed to connect with at the far post.
However, United went ahead in the ninth minute when Boro keeper Mark Schwarzer could only parry Ryan Giggs' left-wing cross-shot and Fletcher slotted home an easy chance from six yards.
The Boro defence looked shaky under pressure as United controlled the first half. The visitors found their men with accuracy while too many Middlesbrough passes went astray.
For the second half Boro sent on Slovakian international Szilard Nemeth for Joseph-Desire Job.
Job had produced a disappointing first-half performance but McClaren could just as easily have withdrawn Hasselbaink.
The former Chelsea striker is in the middle of a lean spell and never looked as though he would get back into a scoring groove.
United substitute Eric Djemba-Djemba had an instant impact on the match when he came on for the injured Cristiano Ronaldo.
Djemba-Djemba had only been on the pitch for two minutes when he supplied the pass for Giggs to score with a low shot that rolled over the line.
A few minutes later Giggs was withdrawn from the action after playing a key role in United's win.
Middlesbrough, surprisingly, forced ten corners in the second half without ever looking as though they would get back into the game.
Jubilant Manchester United fans taunted the home supporters in the final minutes of the game.
"Part-time supporters," they chanted - a reflection on the number of Boro fans who deserted the cause by making their way to the exits before the final whistle.
The United fans followed up with "Champions League, you're having a laugh."
Boro fans had started to look forward with optimism at the prospect of qualifying for the Champions League at the end of the season.
Yet the team will have to show a great all-round improvement on this performance to even challenge the big boys.
MAN OF THE MATCH: Ryan Giggs (Manchester United) - The Welsh wizard scored a goal and tormented the Boro defence with his clever ball skills to show he is still an important figure in the United side.