Belgium international Marouane Fellaini gave the Red Devils the lead on the half-hour mark after getting his head on the end of a brilliant in-swinging cross from Ashley Young.
The visitors then doubled the advantage in the 62nd minute when Lingard, who was included in Gareth Southgate's recent England squad, smashed an effort from the edge of the box into the top-right corner.
Rudy Gestede gave the hosts hope when making the most of a mistake from Chris Smalling in the box with the big target man finding the back of the net from six yards out.
However, a slip from Boro keeper Victor Valdes allowed Antonio Valencia to walk the ball into the net in the dying stages to wrap up all three points for United, who move up to fifth in the Premier League table.
Speaking after the match, Lingard praised the performance from the team and is happy they have managed to come away from the Riverside with all of the spoils.
He was quoted as saying by the BBC: "We had a lot of pace up front today and obviously we had the ball players in midfield to dictate the play. All round it was a good game for us."