Barcelona's Cesc Fabreagas had earlier given Barca a lead in a breathless match in the Santiago Bernabeu that his side looked to be running away with until the leveller.
Varane was Madrid's star all evening, clearing off the line in the first-half and making countless other defensive interventions in an entertaining encounter.
With the second-leg almost a month away, Madrid, who trail Barca by 15 points in the league, will be relieved to avoid defeat and will now look to the Champions League last-16 first-leg against Manchester United in the same stadium in less than two weeks.
Jose Mourinho decided to partner Varane and Ricardo Carvalho in the centre of a depleted defence, with Sergio Ramos and Fabio Coentrao out through suspension and Pepe injured.
At right back Michael Essien was favoured over Marcelo, just back from injury, and Diego Lopez was called up for his debut in goal after he signed from Sevilla last Friday to replace the injured Iker Casillas.
With coach Tito Vilanova in New York receiving further cancer treatment, assistant Jordi Roura took over for a Barca side with far fewer problems, Jose Manuel Pinto was in his customary position in goal for the Spanish Cup, in for Victor Valdes.
And the reserve keeper was immediately called into action to block a Cristiano Ronaldo free-kick after Gerard Pique saw a yellow card on 40 seconds for tripping the Portuguese star on the edge of the area.
He had to be alert again on nine minutes to tip over an Essien cross and Madrid were looking the more direct and dangerous of the two teams in the opening minutes.
The pace was fast and furious and Ronaldo just failed to connect with a Benzema cross in front of goal and then Xavi curled a free-kick onto the crossbar at the other end.
The best chance of the first-half fell to Barca on 22 minutes when Fabregas anticipated a poor back pass from Carvalho and teed up Xavi whose shot was blocked on the line by Varane.
Then at the other end a Benzema snap shot hit the side netting before Messi hit a free-kick over the bar.
At the start of the second period Benzema exchanged passes with Ronaldo before shooting high, but it wasn't long before Barca went ahead.
A Jose Callejon clearance fell to Messi whose quick thinking pass to Febregas left the former Arsenal captain with an easy finish on 50 minutes.
From that point Madrid lost their impetus and Varane had to make a fantastic last-gasp intervention to stop Fabregas from adding another.
Ronaldo stooped to head an Essien cross inches wide but Barca were playing a more measured passing game after the goal and dominating possession.
Gerard Pique was quicker than Ronaldo to a cross when Madrid did break on the counter-attack on 67 minutes and it was Fabregas again at the other end who shot just over three minutes later.
Fabregas then released Pedro Rodriguez who should have doubled the lead on his 200th appearance for Barca, but he badly miscued his shot from close range.
Just when it looked like Barca would leave with victory, Varane popped up to head home a Mesut Ozil cross with nine minutes to go.
Lopez had to save well from Jordi Alba in the closing minutes but a draw was a fair result in the end with all to play for in the Nou Camp on February 27.