He joins Karim Benzema, until 2023, Thibaut Courtois, until 2026, and Federico Valverde, until 2027, in signing contract extensions with the club during the close-season.
The 11th-hour win gave the Selecao a perfect nine points from three matches in the South American championships, and extended their current winning streak to 11 matches.
FIFA World Cup Qualifiers 2022: Richarlison, Neymar score as Brazil beat Ecuador amid off-field crisis
They now lead the round-robin tournament with 15 points, four ahead of second-place Argentina. It appears all but certain that Brazil will qualify for four direct spots for Qatar 2022.
LaLiga: Real Madrid move close to top with win over Valladolid; Atletico suffer surprise loss against Levante
Real Madrid's victory at the Jose Zorilla Stadium was their fourth in a row, three of those coming with clean sheets, which suggests a return to form for a defence that all but clinched them the title last season.
Modric is joint third top scorer at the club and fifth for assists, even though by his own admission his contribution is never truly reflected by those measurements.
Zidane's position has come under scrutiny again after Wednesday's defeat by third-tier side Alcoyano in the Copa del Rey but Madrid responded at Mendizorroza without their coach, or their captain Sergio Ramos, who was out with a knee injury.
LaLiga: Casemiro, Benzema score as Real Madrid beat Granada to move level with Atletico at top of league table
Granada posed problems to Real Madrid on several occasions but their lack of finishing cost them dear.
LaLiga: Atletico Madrid edge past Barcelona to earn title boost; Villarreal hold Real Madrid to a 1-1 draw
Yannick Carrasco finished brilliantly from range after mistakes from Gerard Pique and Marc-Andre ter Stegen left the goal gaping but Barca, and a below-par Lionel Messi, failed to respond at the Wanda Metropolitano.
Neither player will feature in the side to take on Valencia on Sunday. Nor will they be able to join up with their respective national teams during the coming international window as both are required to go into isolation.
Zidane had to experiment in Real Madrid's defence with Sergio Ramos and Dani Carvajal serving suspensions and Marcelo and Nacho Fernández injured.
LaLiga: Karim Benzema's clever assist helps Real Madrid beat Espanyol and go clear at top; Villarreal score win over Valencia
Real Madrid and Barcelona have six games left with Madrid leading by two points. Madrid holds the tiebreaker on head-to-head results in the event they finish level on points.
LaLiga: Real Madrid lacked everything in miserable defeat at Real Betis, says manager Zinedine Zidane
Real Madrid manager Zinedine Zidane called their showing in 2-1 defeat at Real Betis, the worst of the campaign
Casemiro's performance in the Clasico, to contain Lionel Messi, suggests the showing against Manchester City was only a blip for the remarkable player.
LaLiga: Vinicius Junior revels in decisive 'clasico' goal to put Real Madrid on top; Atletico Madrid held by Espanyol
The 19-year-old Vinicius Junior had scored eight goals with Madrid since arriving two seasons ago, but none as big as this one.
LaLiga: Casemiro defends 'incredible' Real Madrid teammate Gareth Bale, says what he does off the field should be respected
Real Madrid midfielder Casemiro says people need to appreciate his team mate Gareth Bale more and stop focusing on what he does away from the pitch.
LaLiga: Casemiro's brace guides Real Madrid to narrow win over Sevilla; Atletico Madrid lose to Eibar
Defensive specialist Casemiro scored his first brace for Real Madrid to ensure a 2-1 home win over Sevilla in the Spanish league on Saturday.
Spanish Super Cup: Real Madrid kick off tournament in Saudi Arabia with comfortable semi-final win over Valencia
Real Madrid midfielder Kroos curled in an exquisite right-footed shot from the corner flag in the 15th minute after spotting Valencia goalkeeper Jaume Domenech out of position
LaLiga: El Clasico losing grandeur as reality checks abound in goalless draw between Barcelona and Real Madrid
Real Madrid travelled to Camp Nou last night to play out a goalless draw vs Barcelona in the LaLiga. This is the first time in the last 17 years that this fixture ended 0-0.
Barcelona and Real Madrid come into the Clasico with 35 points for both teams. Catalans sit top courtesy better goal difference but it would count for nought come end of the season.
LaLiga: Real Madrid coach Zinedine Zidane hints Casemiro could play against Valencia, says he wants best players available
The Brazilian has started all of Real’s 15 games this season as well as every Champions League match. But if he were to earn a yellow card against Valencia he would be a huge loss to Zidane’s side when they visit the Camp Nou on Wednesday.