Real Madrid claimed a small edge on city rivals Atletico Madrid with a tight 2-1 Champions League last-16 first leg win on Tuesday.

Julian Alvarez levelled for Atletico after Rodrygo Goes sent the hosts ahead, but Brahim Diaz stroked home the winner for the record 15-time winners to delight the Santiago Bernabeu stadium.

"I think we played a complete game today, (my) goal was good and it earned us the win, but it's not over," Diaz told Movistar.

"There's still the second leg and we have to give everything, like we did today."

Diego Simeone's Atletico, who lost in the 2014 and 2016 finals against their bitter rivals, kept stars Vinicius Junior and Kylian Mbappe quiet but still came up short.

The Rojiblancos played it safe in the final stages, seeming to accept their one-goal disadvantage for the second leg derby clash at home next week.

"For a moment we had the game under control, but we knew that it would not be an easy match, because they were at home and they have great players," said Alvarez.

"But we know there are 90 minutes to go... it's one goal, and another game, at home with our fans."

Madrid coach Carlo Ancelotti opted for Morocco international Diaz in midfield to replace the suspended Jude Bellingham and selected Fede Valverde at right-back after he was passed fit to play.

The Italian had demanded his side show a better attitude and more commitment than during their La Liga defeat by Real Betis on Saturday and his charges delivered.

Rodrygo pounced after just four minutes, slipping inside Javi Galan to collect Valverde's teasing pass before firing home with his left foot across Jan Oblak and inside the far post.

It was the Brazilian winger's fifth strike of the tournament, habitually shining on the European stage for Madrid, where he boasts 25 goals in 61 appearances.

Rodrygo wanted a penalty when Galan appeared to hold him back in the area but his appeals were waved away.

His compatriot Vinicius came close to netting Madrid's second as he surged into the box but Jose Gimenez blocked his shot well.

- 'We're alive' -

Atletico began to create danger of their own and Valverde hacked away Giuliano Simeone's whipped ball from under his own crossbar under pressure from Samuel Lino.

Alvarez levelled with a brilliant individual goal, dancing away from Eduardo Camavinga on the left of the box and curling his shot past Thibaut Courtois into the top corner.

The former Manchester City striker has been in sublime form in the past few weeks, notching 10 goals in 14 matches and proving why Atletico made him their second most expensive signing of all-time last summer.

Antoine Griezmann and Rodrigo De Paul helped Atletico keep control for long periods, with Madrid finding it hard to take the ball back from their rivals.

That made it all the more surprising when Diaz restored Los Blancos' lead in the 55th minute.

The midfielder left Gimenez on the floor with some quick footwork and carved out the space for a tidy low finish, before leaping into the crowd to celebrate.

Griezmann fired wide and Gimenez over as Atletico looked for a response and Ancelotti brought on 39-year-old midfielder Luka Modric in search of more control.

The Croatian delivered just that and neither side threatened in the final half hour of the match until stoppage time, when Madrid might have secured a third.

Mbappe's cut-back from the right was behind Vinicius who was waiting for a tap-in, and Oblak saved from Modric in the aftermath.

Atletico host Real Madrid next week at the Metropolitano stadium, with the winner facing Arsenal or PSV Eindhoven in the quarter-finals.

"We're alive (in the tie) and we have to correct the mistakes we made and go for it in the second leg," said Atletico midfielder Marcos Llorente.