Real Madrid closed the gap on league leaders Barcelona to one point after a hard fought 3-0 victory at Getafe on Saturday.
The visitors took the lead after 34 minutes when Varane beat Getafe goalkeeper David Soria in the air as the ball trickled into the back in the net.
Madrid's goalkeeper Thibaut Courtois enjoyed a much better game at the other end and produced three fine first half saves to keep his side ahead.
Varane doubled Madrid's lead after 53 minutes when headed home from a Toni Kroos free kick. VAR checked a potential offside for three minutes before awarding the goal.
Modric grabbed a third in stoppage time with the last kick of the game to seal the victory. Barcelona have the chance to regain their four point lead when they travel to Espanyol on Saturday evening.
Madrid boss Zinedine Zidane was full of praise for his goalkeeper for his commanding performance.
"He saved us on two or three occasions in the first half," he said. "He was decisive. He's an important player for the team and he's showing it -- not just in this game, for a long time. I'm happy with his performance."
Goal scorer Varane said: "It was a battle and the team responded well. It was a day to fight and that's what we did.
"We didn't concede goals at the back but that's the work of everyone, when we work together we'll compete for everything. The third goal was a counter attack where we were solid at the back and then we have quality to hurt the opponent."