Without injured talisman Wayne Rooney, United looked almost toothless in attack for much of the game.
It was only after the introduction of Cristiano Ronaldo as a 56th minute substitute for Ji-Sung Park that United began to threaten the well-organised Boro defence.
But United spurned their chances - the worse miss coming in the 66th minute when Ruud van Nistelrooy missed a penalty.
Ryan Giggs swung in a corner from the left which seemed destined for Ronaldo's head until Boro's Lee Cattermole rose to touch the ball away with both hands.
Referee Chris Foy pointed to the penalty spot, only for van Nistelrooy to hit a poor right-foot kick to Brad Jones' right and the Boro goalkeeper guessed correctly to palm the ball away.
Boro had been the better side in a first half in which United failed to get a shot on target.
Fabio Rochemback's 19th minute pass down the left saw Massimo Maccarone get in on the blind side of Rio Ferdinand and he raced on into the United box before his shot was deflected across goal off the England defender.
United goalkeeper Edwin Van der Sar made a brilliant save in the 26th minute to tip away Rochemback's fierce 25-yard shot at full stretch.
From the resulting Stewart Downing corner, Boro skipper Chris Riggott headed narrowly over at the far post.
Ronaldo's introduction sparked some life from United and the Portuguese winger produced his side's first shot on target just after the hour.
Ronaldo raced down the right past Franck Queudrue before unleashing a tremendous 25-yard drive which was beaten away by Jones.
After van Nistelrooy's penalty miss, United continued to press Boro further and further back.
Van Nistelrooy almost made amends for the miss when he turned on a Giggs pass before shooting just over the bar from the edge of the Boro box.
John O'Shea blazed a shot across the Boro penalty area and Jones almost made a hash of taking Kieran Richardson's low cross from the left edge of the box.
But Boro deservedly hung on for a point and United's long drawn-out bid to clinch second spot in the table drags on to the bitter end when they face Charlton at Old Trafford on Sunday.