The lanky 20-year-old, tipped to one day succeed World Cup-winning keeper Iker Casillas, leaped to his left to palm away Pierre Webo's 70th-minute spot-kick and prevent Mallorca from making it 2-1.
Atletico captain Antonio Lopez conceded the penalty when he tangled with Emilio Nsue on the edge of the area and was shown a straight red card.
Mallorca had looked hungrier in the early stages at the Calderon before defender Juan Valera put the home side ahead when he glanced in a header from a Jose Antonio Reyes corner in the 13th minute.
Uruguay striker Diego Forlan, who had not scored in the league since November, doubled the lead just after the half hour when he sprinted on to Fran Merida's through ball and rounded goalkeeper Dudu Aouate.
Tempers frayed late on and Mallorca midfielder Jonathan de Guzman was sent off in the 87th minute for a late tackle on Juanfran which sparked a round of pushing and shoving.
The dismissal took the spark out of the Balearic Islanders and Reyes exploited a huge gap at the back to add a third in stoppage-time.
Atletico's victory lifted the Europa League champions back into the European qualification places in sixth on 30 points at the halfway stage of the season, one ahead of Athletic Bilbao and four behind Espanyol in fifth.
"It was a difficult one and I was lucky to be able to stop it but I am very happy," De Gea said in a television interview.
"It was a very good performance by the team tonight, especially in defence," he added.
Mallorca, coached by former Danish international Michael Laudrup, are ninth on 27 points, the same number as eighth-placed Getafe.
Champions Barcelona extended their lead over Real Madrid to four points when they beat Malaga 4-1 on Sunday and Real were held to a 1-1 draw at bottom side Almeria.
