A stubborn Rostov side refused to role over after the 1-1 draw in Russian Federation in the first leg, and even tested the home side on a number of occasions in a nervy second half.
Paul Pogba limped off injured, as Manchester United advanced to the Europa League quarterfinals, after claiming a 2-1 aggregate win over FC Rostov.
After navigating hard terrain in Rostov-on-Don last week to claim a creditable 1-1 draw in the first leg, it was back to the more familiar surroundings under the floodlights at the Theatre of Dreams for the Reds.
The match will take place at the Old Trafford.
"It was a matter of finishing our chances again".
Manchester United's season has been filled with ups and downs so far.
Marcus Rashford started as striker in United's 1-0 defeat to Chelsea in the FA Cup quarter-finals at Stamford Bridge on Monday night, despite suffering from a bout of illness.
Daley Blind, who has been an ever present figure under Mourinho, also did not the see out the match having picked up a knock to the head.
Mata turned home from close range in the second half after a clever Zlatan Ibrahimovic flick to keep Jose Mourinho's side on track for the final in Sweden in May.
United will be missing injured striking duo Martial and Wayne Rooney, but they will have both Ander Herrera and Ibrahimovic available, despite the pair now serving domestic bans.
Not only had the pitch been unused for several weeks during the winter break for the Russian Premier League, but it was frozen and covered in sand. Mourinho replaced Young with Jesse Lingard, a like-for-like substitution but United were unable to produce any real threats in the second half.
Winning the Europa League carries the prize of Champions League football, which United is also chasing via the English Premier League.
United create enough chances this season and Mourinho for the most part this season has set United up in a way that allows them to attack more than one would usually regard a Mourinho team to play but the goals aren't coming. Russian teams have won just two of their last 26 away games in England and United have never lost to a Russian side on home soil in European competition.
"We'll need to have the same spirit as in the first match", Lyon goalkeeper Anthony Lopes told AFP. The 1-0 win at Old Trafford was otherwise a tepid affair, which they controlled for long spells but in which they failed to take charge on the scoreboard.