Zlatan Ibrahimovic is set to return for the second leg of Manchester United's Europa League last-16 clash with FC Rostov on Thursday evening.
Ex-Chelsea midfielder Mata netted on 70 minutes as he calmly tapped home a clever Ibrahimovic flick from Henrikh Mkhitaryan's cross.
The home side suffered the blow of losing Paul Pogba - who enjoyed a strong first half - to a suspected hamstring injury just after the break and their hold on the midfield suffered slightly as a result.
Rostov could have found an equaliser in the 79th minute if not for Romero, who was on hand once more to save United, this time producing an excellent stop to divert wide Aleksandr Bukharov's close-range header, while he also tipped over Christian Noboa's free kick in the dying seconds. Four of those goals have been scored at Old Trafford.
United's positive attacking intent continued as Ibrahimovic had a free-kick well blocked by Andrei Prepelita before seeing a shot touched over by Medvedev after rounding the keeper when released by a delightful forward pass from Mata.
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It nearly arrived on two occasions when, firstly, Mata's intelligent first-time pass released Mkhitaryan in behind the visitors' defence but his lobbed effort dropped agonisingly wide of the post.
United's injury woes worsened on the 63-minute mark when Blind was forced off and Phil Jones came on as his replacement, with United more desperate for an opener than ever in order to settle any nerves.
United seized control of the game from the very start, and were unfortunate not to take the lead within five minutes. It culminated in a curling effort from Iranian hot-shot Sardar Azmoun, which Sergio Romero had to beat to safety. It took a little while in terms of match time, but Ibrahimovic was back to doing Ibrahimovic things in short order.
Subs not used: De Gea (GK), Young, Carrick, Lingard, Rashford.