The Brazil forward converted a penalty in the 52nd minute at the Santiago Bernabeu to cancel out Ademola Lookman's first-half opener before Vinicius later grabbed the winner with a curling strike in the 72nd.
Surprisingly, the goals were his first against Atletico in the league after 12 scoreless derbies.
Madrid had to hold on for the last 12 minutes when Federico Valverde, who had scored to make it 2-1 before Nahuel Molina levelled for the visitors, got a direct red card for a nasty-looking tackle on Alex Baena.
But Alvaro Arbeloa's team saw out the final minutes to ensure second-placed Madrid (69) stayed within four points of Barcelona with nine games remaining.
"Another great game by Vini, it was an example of his character, his talent," Arbeloa said.
"It was a great goal that gave us a win in a difficult moment. I am lucky to have him on my team. We remain in the league fight. Mission accomplished."
The Catalan giants edged Rayo Vallecano 1-0 at Camp Nou earlier on Sunday to keep up their winning form before the international break.
Ronald Araujo headed in the game's only goal in the 24th from a corner kick, and goalkeeper Joan Garcia's impressive performance showed why he is most likely heading to the World Cup with Spain.
"It was important to get these three points, even if it wasn't our best game," GarcÃa said.
"We needed to win, and now what the others do doesn't depend on us."
Araujo stepped away from soccer from last November to early January because of what he said was a bout of depression caused by a longer struggle with anxiety.
"I am feeling good, physically too," Araujo said after his first league start since returning, in place of injured Jules Kounde.
"I am always here to help the team, whether I play at centre back or right back ... I always felt the support of Barcelona's fans."
Elsewhere, Alaves came from three down to win 4-3 at Celta Vigo and move out of the relegation zone, while Athletic Bilbao went ninth after a 2-1 win over fifth-placed Real Betis.
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