Lukaku's goal before an Alexis Sanchez strike on Saturday helped United remain on course to finish second in the league behind runaway leaders Manchester City.
The goal was textbook Lukaku, as he finished off a nice passing play between Alexis Sanchez and Jesse Lingard.
The clean sheet was De Gea's 16th of the Premier League campaign so far.
The goal came after only four minutes and that set the tone for the rest of the first-half as United dominated.
Lukaku has certainly won over doubting United fans over the second half of the season and Mourinho will possibly do likewise if he can delay City's title party on Saturday.More news: China's space station set for re-entry, hurling towards Earth
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Mourinho is delighted to see the 24-year-old performing at the peak of his powers, but believes he will get even better as he continues to experience life at the very top. "The first half we played very well, we kept Swansea back, we scored, we played lovely, it was ideal".
'First half they didn't cross the midfield line, didn't have one shot.
United hardly got out of second gear in the final 10 minutes, while Jose Mouirnho introduced Scott McTominay as they saw out the remaining stages easily. We arrived in many unsafe positions, we scored two, we should have scored at least one more.
He does at least give The Swans credit for our fightback in the second half. "But it's fine. Every point is vital because we want to stay in second place".
He has also been an ever-present between the United sticks, playing in all 31 Premier League matches for the Old Trafford club, while on the European stage, De Gea mustered six appearances.
Liverpool came from behind to win at Palace in manager Juergen Klopp's 100th league game in England and move five points ahead of fourth-placed Tottenham Hotspur, who visit fifth-placed Chelsea on Sunday.