The 38-year-old Modric unleashed a powerful strike that grazed the post before finding the net in the 81st minute.
The former Ballon d'Or winner had entered the fray just six minutes earlier with with the leaders stymied in attack without injured top scorer Jude Bellingham.
Madrid were heading towards a second straight draw after being held 1-1 at Rayo Vallecano in the last round.
Another stumble would have given Barcelona reason to hope that they might just be able to mount a challenge after they overtook Girona for second place on Saturday.
But Madrid's victory keeps them eight points above Barca and nine clear of the season's surprise package Girona.
"It is what always happens. We never give up. We have shown it many times, that this is a part of Real Madrid's DNA," Modric said.
"It was important not to let points get away because Barcelona would have closed the gap and we couldn't allow that."
Bellingham, the league's top scorer with 16 goals, has missed three games with a left ankle sprain.
Nico Williams was sent off after two yellow cards in quick succession to leave Athletic Club down to 10 players just before halftime in their 3-1 loss at Real Betis.
The Spain winger went into the book for a foul and compounded his crime by earning a second booking for his sarcastic applause of the referee.
The loss meant Athletic failed to take advantage of Atletico Madrid's 2-2 draw at bottom side Almeria on Saturday.
Athletic remain in fifth place in La Liga, three points behind Atletico.
Chimy Avila scored his first goal for Betis since joining from Osasuna in the winter transfer window to give his side a 13th-minute lead.
Yuri Berchiche added an own-goal before Williams was sent off in the 40th minute.
Gorka Guruzeta's goal early in the second half gave Athletic some hope, but Betis midfielder Johnny Cardoso added Betis's third with a strike from the edge of the area in the 67th minute.
Darwin Machis's goal deep in injury time snatched Cadiz a 2-2 draw with Celta Vigo in a meeting of two relegation-threatened sides.
Iago Aspas and Williot Swedberg gave Celta a 2-0 advantage before Juanmi Jimenez pulled one back for the hosts in the 66th minute.
Rafa Benitez's side were still eyeing victory until Machis curled a shot in from the corner of the area just before the final whistle.
"You think you have it in the bag, you are up 2-0, and they score two goals on plays we could have stopped," Benitez said.
"We missed an opportunity. We didn't know how to manage those final minutes."
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