The score was 0-0 at the time of Pogba's exit and United went on to win 1-0 courtesy of Juan Mata's 70th-minute goal, completing a 2-1 aggregate victory that sent them into the quarter-finals.
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.
They look to be heading through to the next round now, after Mata found the back of Rostov's net.
Pogba fired a free-kick from the left into the stands as the half wore down while the opening period ended with a rare attack for Rostov as Alexandr Erokhin placed his shot wide of Sergio Ramero in the United goal.
The Reds strongly appealed for a penalty on 26 minutes when Henrikh Mkhitaryan, who scored the crucial away goal in the first leg, appeared to be shoved in the back by the Rostov keeper when competing for a high ball but Lithuanian referee Gediminas Mazeika ignored the claims.
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On United's performance against Rostov, Mata added: "It was a matter of finishing our chances again. We have the same players in the last match plus (Zlatan) Ibrahimovic returning for the Europa League".
Rostov weren't without their threat, either, and Sardar Azmoun tested the skills of Romero before coming off to be replaced by Aleksandr Bukharov.
There was no sign of Rooney at Wednesday's training session after he sustained a knock in a training-ground collision with Phil Jones, and Mourinho confirmed that he is still receiving treatment.
The visitors still needed only a goal to take the game into extra time, though fortunately Romero wanted extra time as much as the rest of us stood watching.
United will find out on Friday who they will play in the quarter-finals, with the draw taking place at 12:00 GMT.