Cristiano Ronaldo's second-half penalty was enough to send Manchester United through to the FA Cup semi-finals.
Ronaldo coolly converted his penalty
Ronaldo was chopped down from behind by Jonathan Woodgate with the winger clinically dispatching the spot-kick.
The excellent Mark Schwarzer had twice thwarted Wayne Rooney when the striker had been put clean through with Boro on the back foot throughout.
Tempers frayed in injury time with substitute James Morrison dismissed for a reckless lunge on the match-winner.
United's progression to the last four equals the record number of 25 appearances in the semi-finals - set by Arsenal - and the Premiership leaders will now meet bottom side Watford in the next round.
The home side, depleted and playing their fourth game in 10 days, controlled much of their quarter-final, with Middlesbrough intent on frustrating their opponents and catching them on the break.
United looked in no mood to let the game go the distance and quickly set about penning Boro in their own half - not that an edgy Middlesbrough side were eager to throw men forward at the other end.
In truth, their compact and stand-offish approach suggested they would be more than happy to take their chances in extra-time or penalties.
The visitors, who have not managed to get through an FA Cup round at the first time of asking this season, were restricted to long-range, speculative efforts that seldom troubled Tomasz Kuszczak, while Mark Viduka was too often a one-man cul-de-sac.
Marshalled by the solid Woodgate, Boro stood firm to the attacks of Ronaldo and Rooney.
However, Boro's hard work in the first half was almost undone by Rooney shortly before the break. The striker was superbly thwarted by Schwarzer after being put clean through by Ryan Giggs in the only chance of note in an uninspiring opening 45 minutes.
Middlesbrough, perhaps realising that their negative approach could not hold out a relentless United attack for a further 45 minutes, created a fine chance of their own 10 minutes after the interval.
Carlos Queiroz was at the centre of the off-field argument
Fine work from Viduka down the left resulted in a shot from Stewart Downing that was horribly slashed wide on his weaker right foot.
Ronaldo hit the outside of the post from an acute angle after being shunted wide by the excellent Schwarzer and the Aussie then kept out Rooney with an outstretched boot.
But there was little Schwarzer could do about the winner as Ronaldo clinically converted the penalty he had won.
Boro were incensed at the decision, but Woodgate's only mistake of the match was ugly, awkward and effectively, costly.
With Boro beaten and dejected, Morrison saw red for a late lunge on Ronaldo.
That challenge sparked a melee in which Rooney could easily have been sent off himself after needlessly getting involved in the ruckus and the brawl spilled on to the sidelines with both benches becoming embroiled in the argument.
But Rooney remained on the pitch and United extended their unbeaten run to 13 games.
Man Utd: Kuszczak, Brown, Ferdinand, Vidic, Heinze, Ronaldo, Carrick, Giggs, Richardson (Park 60), Smith (O'Shea 71), Rooney.
Subs Not Used: Heaton, Cathcart, Eagles.
Booked: Smith, Rooney.
Goals: Ronaldo 76 pen.
Middlesbrough: Schwarzer, Xavier, Woodgate, Pogatetz, Taylor (Huth 88), Cattermole (Morrison 62), Boateng, Arca (Rochemback 69), Downing, Yakubu, Viduka.
Subs Not Used: Jones, Lee.
Sent Off: Morrison (90).
Booked: Xavier, Woodgate, Pogatetz, Boateng, Rochemback.
Ref: M Dean (Wirral).