Juan Mata has said that "it is not by chance" that Manchester United are now unbeaten in their last 18 Premier League matches.
But an Antonio Valencia tap-in after a slip by Victor Valdes made sure the visitors took all three points.
United's cruel April fixture list sees them host in-form teams West Brom and Everton in quick succession, before travelling to Sunderland on the 9. In the 62 minute, Jesse Lingard scored an outside the box goal to give United a satisfying (2-0) lead.
Rudy Gestede's goal was the first that Middlesbrough have scored in the Premier League in 509 minutes of action.
United now haven't lost a league game since October 23, and have finally clambered into the top five after what seemed like eons in sixth.
As a two-week global break brings a halt to club football, United find themselves in fifth place, some four points behind fierce rivals Liverpool, who now occupy fourth. United have an enormous possibility to be in the top four and claim a spot in the Champions League.
Rangers lose two star players for Zamalek battle
Godwin Aguda made it 2-1 for the home side, but there were no more goals in the encounter. Rangers could not celebrate the 2-1 victory as it could not guarantee them progress.
The clash between Manchester City and Manchester United at the Etihad Stadium was postponed in Feburary because of United's involvement in the EFL Cup final against Southampton, a game they won 3-1.
"It is fantastic because we manage in the same week, to go to the quarter-finals of the Europa League which is an important target for us".
Mourinho named former captain Keane, along with Ryan Giggs and Paul Scholes, as examples of the type of players who helped make Alex Ferguson's reign at Old Trafford so successful.
One of those came 10 years to the day before United's first trip to the Riverside in the 2010s, but it was in the FA Cup rather than the league. However, they can now exclusively focus on the EPL and the Europa League.
United moved above Arsenal into fifth place with an eighth win in its last 11 matches in all competitions. Chelsea is ten points ahead second place Tottenham, and they keep demonstrating every week there is no stopping them.
The two managers have now brought their fascinating battle to the Premier League. "I have to admit it was hard for us", Mourinho solemnly intoned.