The setback for Jose Mourinho's side, after a brilliant last-minute free-kick from Santi Cazorla, halted their 11-match winning run and gave Barca a sliver of hope they can rein in their arch rivals and secure a fourth straight La Liga title.
Real, on 71 points to Barca's 63 with 11 games left, face a tough trip on Wednesday to Villarreal, who are fighting to preserve their top-flight status after Sunday's 1-0 reverse at Levante left them three points above the relegation places.
It will be a baptism of fire for Miguel Angel Lotina, Villarreal's third coach of the campaign, hastily hired on Monday to replace the sacked Jose Molina.
"It seems to me that drawing a game is part of the competition," Mourinho told a news conference after the Malaga game.
"We all know that there are 11 matches left and 33 points up for grabs, which means the title race is still open," added the Portuguese.
"Tomorrow will be another day and on Wednesday there is another match."
Barca are trailing Real mainly due to their patchy away form, although they went some way to correcting that with a 2-0 win at Sevilla on Saturday.
Pep Guardiola's side have won 12 and drawn one of 13 home matches this season, scoring 53 goals and conceding just five.
On the road, by contrast, they have won seven, drawn five and lost two, managing only 24 goals for and letting in 14.
"We are this far behind because up to now we have been slipping up away from home," full-back Daniel Alves told reporters after training on Sunday.
"Getting a balance between home and away games lets you get closer in the battle for the title," added the Brazilian. "At the key part of the season we are starting to get this balance back."
BACK TO EARTH
Valencia strengthened their grip on third with an impressive 3-0 win at Athletic Bilbao on Sunday, striker Roberto Soldado netting a hat-trick, and host bottom side Real Zaragoza on Wednesday.
Defeat brought seventh-placed Bilbao back to earth after they eliminated Premier League leaders Manchester United from the Europa League midweek and the Basque club play at Atletico Madrid on Wednesday.
Qatar-owned Malaga, who are fifth, level on points with fourth-placed Levante, host Rayo Vallecano on Thursday with their tails up after Sunday's draw in the Spanish capital.
"We played a spectacular match, very complete, and to get a result like that, right at the end of the game and at the Bernabeu, is really nice," Cazorla told reporters.
"It's important to score but I am happier about getting a point at a stadium where nobody else has managed it this season except Barcelona," he added.
"It was the right moment for us to lay down a marker and achieve good things in big games."
