Real made it five wins out of five thanks to a Karim Benzema double and a sublime curler from Kaka and lead with 15 points, ahead of Barca on goal difference.
Sevilla, who won 4-0 at Athletic Bilbao, are third on 12, while substitute Maxi Rodriguez struck in added time to earn struggling Atletico Madrid a 2-2 draw at Valencia.
In a match littered with yellow cards, Malaga defender Weligton looked fortunate to stay on the pitch after TV replays showed him treading on Messi's ankle.
"It was a very aggressive match that took a lot out of us," Barca coach Pep Guardiola told a news conference.
Asked whether the La Liga campaign was already a two-horse race between Barca and Real, he added: "Madrid has economic might but we have too and the players make the difference. In that sense we have a big advantage."
Tenerife are dubbed Real's 'Cursed Island' by the Spanish media after the Canary Islanders twice deprived the Madrid club of the league title in the early 1990s.
After a closely-fought first half with few clear chances, Benzema rose early in the second period to nod in Xabi Alonso's cross and then outmuscled defender Manuel Martinez and curled a precise shot into the far corner.
"We were very bad in general in the first half and the substitutions obviously helped," Real coach Manuel Pellegrini said at a news conference.
"It was clear that Kaka gave the team a boost but we have a Champions League match (against Olympique Marseille on Wednesday) and we tried to win the game with him."
