Goals by Boro's record signing Afonso Alves either side of halftime, the champions needed an equaliser from Wayne Rooney (right) 16 minutes from time.
Complete Coverage: English Premier League
United levelled when Park Ji-sung crossed from the right for Rooney to snatch a point.
"It was a fair result," United manager Alex Ferguson told Sky Sports.
"There was a period in the second half when I had to re-arrange the back four and we could have lost two or three goals. But it's in the nature of our club to never give in, it's a marvellous quality and they proved it again today.
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