With the result, the Red Devils leapfrog arch-rivals Arsenal in the league table.
Manchester United snatched an important 3-1 away win against Middlesbrough to jump to the fifth spot in the English Premier League (EPL) at Riverside Stadium here on Sunday.
Belgian midfielder Marouane Fellaini opened the scoring for Manchester United 30 minutes into the first half, before Jesse Lingard scored again for the visitors at the 62-minute mark, reports Efe.
Middlesbrough's Rudy Gestede hit back 15 minutes later, before Antonio Valencia scored the decisive third goal in the third minute of added time.
Currently, Manchester United hold the fifth position in the league table with 52 points from 27 games, after spending a few weeks stuck in sixth position, despite a good winning streak.
"I think we started the game really well; (Middlesbrough goalkeeper Victor) Valdes made three fantastic saves before our first goal. We controlled everything before our second goal and they then changed to play with (Rudy) Gestede and (Alvaro) Negredo," Mourinho said, according to United's website.
"They started putting long balls in to the box. We decided to defend with an extra defender, but I think with the mistakes of letting them push us too much into our box.
"Then it was a fighting 15 minutes where they didn't have chances but they were close to the dangerous areas, so the game was alive until the last seconds."
Jose Mourinho-coached United have therefore revived their chances to end the season within the big four, and secure a direct ticket to the Champions League.
On the other hand, Middlesbrough seem to have settled for relegation as the season approaches its final stretch, as they currently hold the 19th position with 22 points.