United hit back with a second-half equaliser to force an Old Trafford replay on Monday March 19.
In view of their congested fixture programme, no doubt the extra game is a burden for manager Sir Alex Ferguson.
Middlesbrough have become replay specialists this season and should they reach Wembley it will certainly be by the hard way.
The Old Trafford match will be their fourth replay in the competition this season.
Manchester United were forced into a late change when the goalkeeper Edwin Van der Sar injured a calf in the warm-up and was replaced by Tomasz Kuszczak.
United started the game as strong favourites even though Middlesbrough have a brilliant record against them in recent years with five wins and two draws from 12 games.
United star Cristiano Ronaldo was barracked by the home crowd right from the start following his controversial penalty in a Premiership game at the Riverside Stadium earlier this season.
Middlesbrough players and fans felt the Portuguese star won the spot-kick with a dive.
United went ahead after 23 minutes when Ryan Giggs split open the defence and Wayne Rooney shot into a corner of the net.
Middlesbrough struggled to hit form and United certainly looked the more dangerous side in the first half.
An unmarked Giggs was unlucky when his first-time shot beat Mark Schwarzer but hit the far post.
On the stroke of half time, local hero Lee Cattermole sent the home fans wild with a brilliant equaliser.
With a pass from the outstanding Julio Arca, Cattermole showed a delightful first touch and a powerful volley into the net.
Middlesbrough raised the tempo and tension immediately after the break when skipper George Boateng put them ahead with a header at the far post.
Boateng has often played this season throughout a pain barrier. On this occasion he was a hero to the fans, though United would have been bitterly disappointed over the slack marking that led to the goal as there were no defenders in sight at the far post when Stewart Downing sent over a corner from the right.
Middlesbrough fans began an optimistic chant of "We're going to Wembley" but United drew level with a penalty scored ironically by Ronaldo.
Referee Rob Styles immediately pointed to the spot where Boateng handled and Ronaldo took his time before shooting to Schwarzer's right.
In a thrill-a-minute finale, both teams went flat out for a winning goal but they will have to do it all again at Old Trafford before the semi-finalists are known.