Suarez, who has been impressive for Atletico Madrid this season, broke the deadlock 15 minutes into the match, firing home after Marco Llorente played him through to score his 17th goal of the La Liga campaign.
Atletico Madrid had several opportunities to double their lead, so had Real Madrid to find the equaliser. However, both goalkeepers - Thibaut Courtois and Jan Oblak - put in terrific performances, and it seemed Diego Simeone's side would take home all three points.
However, Benzema struck in the 88th minute, slamming the ball into an empty net following a wonderful one-two with Casemiro.
The draw means Atletico Madrid now have only a three-point lead over second-placed FC Barcelona, although they can still extend that to six if they win the game in hand.
Meanwhile, a defeat would have been a disastrous result for Real Madrid, who sit third in the table, five points behind Atletico Madrid and two behind Barcelona.
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Meanwhile, Atletico Madrid host Athletic Club in La Liga on Wednesday in their next match, while Real Madrid entertain Elche at Estadio Alfredo Di Stefano on Saturday.