Barca coach Ernesto Valverde used Messi's absence to hand starts to big signings Ousmane Dembele and Phillipe Coutinho and both responded to the challenge with Dembele setting Coutinho up for Barca's second goal of the game.
By then the league leaders had opened the scoring thanks to Luis Suarez, who with his goal in La Rosaleda has now scored against every side that he has played in the Primera Liga since his arrival in 2014.
Barca's task became much easier when Malaga midfielder Samu Garcia was sent off for a wild challenge of Jordi Alba with an hour still remaining in the game and in the second half they were content to conserve energy ahead of Wednesday's Champions League tie at home to Chelsea.
Second-placed Atletico Madrid remain 11 points behind Barcelona after a 3-0 win at home to Celta Vigo.
Antoine Griezmann was given the award for player of the month for February before the kick off and celebrated by opening the scoring following a wonderful piece of control on the stroke of half time.
He then set Vitolo up for Atletico's second in the 56th minute, a minute after Celta had hit the woodwork, and Angel Correa sealed the win seven minutes later.
Real Madrid remain third after Cristiano Ronaldo scored twice away to Eibar in a game which Madrid coach Zinedine Zidane admitted they didn't deserve to win.
However, after Eibar had pegged Madrid back in their own half for much of the opening 45 minutes Ronaldo took advantage of a defensive error and a pass from Luka Modric to open the scoring.
Ivan Ramis equalized five minutes into the second half with a powerful header, but another error allowed Dani Carvajal to cross from Ronaldo to score the decisive goal 6 minutes from time.
Valencia all but assured Champions League football next season thanks to two goals from Rodrigo Moreno, who now has 12 this season.
The win gives Valencia an 11 point cushion over fifth-placed Sevilla, while Sevilla's season now hangs on the result of Tuesday's trip to Old Trafford.
Villarreal remain sixth after a 2-0 win away to Las Palmas thanks to second half goals from Carlos Bacca and Nicola Sansone, a result which leaves Las Palmas adrift in the relegation zone.
Raul Garcia scored twice as Athletic Club enjoyed a relatively easy 2-0 win at home to Leganes to end any lingering relegation fears.
Meanwhile Espanyol scored two second half goals through Leo Baptistao and Gerard Moreno to cancel out Willian Jose's first half opener for Real Sociedad who continue to make too many defensive errors.
Finally, Coke's 79th minute header gave Levante their first win in 16 games as they won 1-0 away to Getafe to give Paco Lopez a win on his debut as coach.
