Atletico have been beaten by the record 15-time European champions in both of their Champions League final matchups and have won only three of 11 meetings with their city rivals in UEFA competitions.
Also on Tuesday, Arsenal made a massive step toward a quarter-final spot with a 7-1 win at PSV Eindhoven.
"It's a massive result away from home in a competition that we love, that we miss for so many years," Arsenal manager Mikel Arteta said. "Today is a really special night for us."
On a good night for Premier League teams, Aston Villa won 3-1 at Club Brugge, and Borussia Dortmund drew 1-1 with Lille.
A tense encounter in the Spanish capital was decided by a moment of individual brilliance from Diaz.
It was a superb run and a well-placed finish by Rodrygo that gave Madrid the lead. Then a nifty move and a precise shot by Julián Álvarez equalised for Atlético just past the half-hour mark.
Diaz scored the winner after squeezing past a couple of Atletico players and curling a low strike into the far corner in the 63rd minute.
Diego Simeone's team lost their finals to Madrid in 2014 and 2016 and were eliminated the other two times they faced off in the knockout rounds - in the 2015 quarter-finals and 2017 semi-finals.
Arsenal got off a shaky start against PSV and Jurrien Timber scored against the run of the play with a header at the far post. The London team never looked back.
Seventeen-year-old Ethan Nwaneri doubled the lead in the 21st after his teammates combined well in the area to set him up. Mikel Merino then made the most of confusion in the box to make it 3-0.
A silly foul from Thomas Partey on Luuk de Jong in the box gave PSV some hope before halftime and Noa Lang converted.
But PSV crumbled once back from the locker room. Arsenal captain Martin Odegaard scored twice, with Leandro Trossard and Riccardo Calafiori adding more lustre to the win.
Last season's runner-up Borussia Dortmund are evenly matched with Lille ahead of the second leg after Hakon Arnar Haraldsson's goal salvaged a 1-1 draw for the French team.
Dortmund led thanks to Karim Adeyemi's low shot from outside the box in the 22nd minute, but Canada forward Jonathan David sliced open the Dortmund defence with a through ball in the 68th for Haraldsson to level the score.
Aston Villa shook off their poor away form with their win in Belgium.
A turning point came in the 82nd minute when Club Brugge defender Brandon Mechele beat his own goalkeeper with the teams tied 1-1. Mechele slid to stop a cross from Morgan Rogers, only to deflect into the back of the net.
Before that, the Belgian side had looked solid, enjoyed most of the possession and created the best chances in the second half.
Looking demoralised, the hosts then conceded a late penalty that was converted by substitute Marco Asensio.
Villa had suffered two away defeats in the group phase of the tournament, including one at Club Brugge. In the Premier League, the team has lost seven of 13 away matches.
On Wednesday, it will be Paris Saint-Germain hosting Liverpool, Inter Milan visiting Feyenoord, Benfica taking on Barcelona, and Bayern Munich welcoming fellow German club Bayer Leverkusen.
