After three games matching up a back three against similar shapes, Mourinho may well decide to revert back to a 4-2-3-1 for Boro, with the midfield nearly picking itself due to the absences of Herrera and Pogba.
Goals from Marouane Fellaini, Jesse Lingard and Antonio Valencia were enough for the visitors as they bounced back from their latest league setback against Bournemouth at the beginning of March.
Jose Mourinho has never been a manager excessively fond of aesthetics, but at the moment he seems to nearly delight in collecting hard and unattractive victories.
United moved above Arsenal into fifth place with an eighth win in its last 11 matches in all competitions.
United were without Paul Pogba, Ander Herrera and Zlatan Ibrahimovic, so Marcus Rashford led the line.
Mourinho refused to comment, but Middlesbrough caretaker manager Steve Agnew insisted his players were reacting to provocation after a stoppage-time bust-up between United defender Eric Bailly and Rudy Gestede, which initially appeared to include the duo biting each other before replays showed it was only a heated clinch.
A hard test but United pass, if only just: It's always challenging to come up against a side with a new manager, particularly when you have played 15 more games than your opponent, but Manchester United handled the task well and fully deserved the three points, even if it wasn't entirely convincing at times. United are ahead, Fellaini spins away at the back post and heads in from Young's cross!
England winger Lingard then took centre stage as he let fly from 25 yards and found the top right-hand corner with an outstanding effort. That intent was leaving United space to exploit on the break, with ponderous play from Rashford forgotten after Lingard sent the travelling fans wild.
Mourinho decided a 2-0 lead was plenty and withdrew Mata in favour of Marcos Rojo. Gestede gives Boro a lifeline!
Among the marvelling about Ibrahimovic's goalscoring this season, the inevitable sub-plot has been the fear that United are too reliant on the 35-year-old.
Hargreaves said: 'Well, I think he's finding a way to win games. Yes, I need two days.
Finishing in the Premier League top four would also give them qualification but Mourinho says a trophy is the better way to do it, even if it's risky.
The decision to part company with Karanka was clearly a hard one for Boro chairman Steve Gibson, who has reiterated that it was a mutual call and said this week that he would "remain friends" with his former manager.
Boro's response to the goal was creditable but, like so many times this season, intricate build-up play was not matched by an end product.