United headed into Thursday night’s round-of-16 second leg needing a result after a 1-1 first-leg draw at Old Trafford.
Milan carried a valuable away goal back to Italy after Simon Kjaer’s injury-time header had cancelled out Amad Diallo’s opener in that game, and the delicate balance of the tie was reflected in a cagey opening 45 minutes in Milan.
With United needing to score to stay in the contest, Solskjaer made a half-time change as Pogba returned from his injury layoff in place of Marcus Rashford – and it proved an inspired change.
Three minutes into the second half, Milan failed to clear from inside their own penalty area as United kept the pressure on. The ball fell to Pogba on the left, and he faked before clipping a glorious finish high past Gianluigi Donnarumma at the near post to hand United the advantage.
Milan responded by sending on 39-year-old former United striker Zlatan Ibrahimovic – just back from injury himself – and he went closest for the Rossoneri.
Dean Henderson will feel he could have done better with Kjaer’s first-leg goal, but made amends with a superb point-blank save to deny Ibrahimovic off a towering header from close range.
United held on to see out the result and secure a spot in the Europa League quarter-final draw, boosting Solskjaer’s hopes of winning his first trophy as Red Devils manager.