Benzema again proved a bright spot in a disappointing season for his club, scoring his fifth goal in four matches to cancel out an opener by right back Jonathan Silva.
The France striker also snatched recent wins for Madrid with late goals against Huesca and Eibar.
Madrid remains third in the standings, 13 points adrift of Barcelona, which is on course to retain its title with six games left and a nine-point lead over Atletico Madrid.
Coach Zinedine Zidane already said Madrid had little to play for this season, adding over the weekend that his squad was set to be culled at the end of the campaign.
Goalkeeper Keylor Navas, whose future has been in doubt since the arrival of Thibaut Courtois last year, said on Monday that the players had more to play for than just trophies.
"We have our pride and our love for this shirt, which is worth more than any title," Navas said. "It has been a complicated season for everyone.
"We have gone out there to win games, but they have gotten away from us. It is difficult to explain. We are all sad for the situation."
Other than a shot by Marco Asensio saved by goalkeeper Ivan Cuellar, Leganes had little trouble keeping in check Madrid's attack in the first half.
The hosts went ahead just before halftime when Martin Braithwaite won the ball in a crowded area and passed to Silva, who curled a shot around Navas into the corner of the net from the edge of the penalty box.
A flash of skill from Luka Modric then set up the equalizer in the 51st minute.
The Ballon d'Or winner turned quickly before slipping a pass through the defense to Benzema. His first strike was blocked by Cuellar, but the France forward pounced on the rebound and fired it home.
It was Benzema's team-leading 27th goal in all competitions this season.
His increasing status since the departure of Cristiano Ronaldo at the end of last season is in stark contrast to the fall from grace of Gareth Bale.
Bale played only the last 10 minutes against Leganes and, after falling out with the fans this season, he could be one of the stars the club will look to move on.
"I didn't like our first half, but I think our second half was better," Zidane said. "At the end we managed to draw, but we could have played much better. That is for sure. The sensation is not good."