Jose Mourinho's side will now hope to go on and win their second trophy of the season after securing the EFL Cup with a dramatic 3-2 win over Southampton last month.
Rostov were struggling to string passes together with the hosts very much in control midway through the first half. An outswinging corner by Daley Blind was met by a powerful Marcos Rojo header, though Rostov keeper Nikita Medvedev was on hand to deny both the Argentine and Zlatan Ibrahimović on the follow-up. With the angle tight, the Swedish striker was unable to find the net and his shot scrambled wide.
Ibrahimovic was then kept out by the woodwork again 11 minutes before the break, drilling a fierce effort onto the right-hand post after cleverly sidestepping Miha Mevlja in the area.
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LUIS SUAREZ'S incredible run of winning when he finds the back of the net ground to a resounding halt on Sunday... after 72 games. In fact, in the 72 games Suarez has scored in for Barca, the Catalan giants won 67 times, drawing five. losing none.
United were forced into an early change just three minutes after the restart as Pogba came off with an injury and was replaced by Marouane Fellaini.
Rostov barely threatened in the opening exchanges but they almost took the lead in the second half when Sardar Azmoun forced a save from United stopper Sergio Romero.
United heeded the warning and pressed hard for the opener, with Ibrahimovic heading over from Antonio Valencia's cross.
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Redshirt freshman Dazon Ingram led Alabama with 17 points before fouling out of the contest in the final two minutes. It committed 15 turnovers, Isaiah Briscoe struggled offensively and the team shot 6-for-16 from 3-point range.
The resurgent visitors, now seventh in the Russian Premier League, began to offer more of a threat which opened the game up in United's favour and the Reds' patience was rewarded in the 70th minute.
But United took a lead that their first-half play deserved as Mata slotted home from close range, on 70 minutes, after Ibrahimovic's back-heel flick from a good, low Mkhitaryan cross from the right fell kindly for the Spaniard at the back post.
That chance marked the switch to a more purposeful set-up from the away side, but that only served to give United more space to attack.
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A spokesman at Mumbai's Saifee Hospital said: "We are trying to get her fit enough to fly back to Egypt as soon as possible". Suffering from a thyroid problem, the 37-year-old Eman gained huge weight, which made it impossible for her to move.
Rostov came inches from levelling on the night and on aggregate just eight minutes later.