Wayne Rooney produced two wonder goals as Manchester United made impressive progress into the FA Cup fifth round.
John O'Shea put holders United in front after 10 minutes from close range.
Rooney then brilliantly lobbed Mark Schwarzer from fully 40 yards after 67 minutes, before firing home a stunning volley with nine minutes left.
Boro's best chance came after 31 minutes, but Roy Carroll dived to save well at the feet of Boudewijn Zenden from only eight yards.
United made a flying start and went ahead after 10 minutes, with O'Shea firing powerfully into the top corner past Schwarzer after Middlesbrough struggled to clear.
Middlesbrough stuck to their task and were guilty of wasting a glorious opportunity to equalise after 31 minutes.
Rio Ferdinand's error let in Zenden, and he exchanged passes with Jimmy Floyd Hasselbaink but was denied as Carroll dived bravely at his feet to save.
But United were in the ascendancy and could have extended their lead before the interval, with Schwarzer blocking from Rooney and Gabriel Heinze turning wide when unmarked at the far post from O'Shea's flick.
Middlesbrough were pushed back after the break, and United almost finished off a sweeping break with the second after 55 minutes.
Carroll's throw released Cristiano Ronaldo, but his pass to Ryan Giggs carried just too much weight and Schwarzer was able to intercept.
Schwarzer need to perform heroics again to save from O'Shea inside the six-yard box - but he was powerless to prevent Rooney adding United doubling their advantage with a brilliant individual goal after 67 minutes.
Gary Neville released the England teenager, who spotted Schwarzer advancing off his line and delivered an audacious chip to perfection from 45 yards.
And Rooney provided another piece of magic after 81 minutes to crown an impressive United display.
Louis Saha flicked on Carroll's clearance and Rooney met it with a stunning volley which flashed high past the diving Schwarzer.
Man Utd manager Sir Alex Ferguson:
"The first (Rooney) goal was precision. They were both marvellous goals. The three goals were very good goals.
"It was a tricky tie as Middlesbrough have a good record at our ground but the players applied themselves very well. I thought they played with a great tempo.
"I was pleased with the performance overall. The whole team played well."
Middlesbrough manager Steve McClaren:
"It was always going to be difficult here and we came across a Manchester United side which was very good on the day.
"In Wayne Rooney they had the difference on the day. He is a magnificent player.
"You need to score first. Whenever we have done well here we have done that. We had a magnificent chance to equalise. It was a good chance, we didn't take it and we got punished."
Man Utd: Carroll, Gary Neville, Ferdinand, Brown, Heinze (Silvestre 79), Ronaldo (Miller 72), Phil Neville, O'Shea, Fortune, Giggs (Saha 65), Rooney.
Subs Not Used: Howard, Scholes.
Goals: O'Shea 10, Rooney 67, 82.
Middlesbrough: Schwarzer, Reiziger, Southgate, Cooper (McMahon 79), Queudrue, Morrison, Parlour, Doriva (Job 45), Zenden, Downing, Hasselbaink (Graham 83).
Subs Not Used: Nash, Parnaby.
Ref: S Dunn (Gloucestershire).