David Murphy scored for Boro three minutes into the second half but Matthew Williams equalised just two minutes later.
United were reduced to 10 men for the final 15 minutes after James Davis was sent off for a second bookable offence, but Boro failed to make their advantage count.
The reserves are now one point behind Sunderland and Aston Villa with a game in hand. They must win both remaining games against Birmingham City (h), next Monday, and Manchester United (a), next Thursday to make sure of the title.
However, Sunderland play Aston Villa in the last game for the two clubs, so if they draw just one win will be sufficient for Boro. They play next Friday