Alaba fired home a powerful left-foot drive in the first half before Lucas Vazquez made the game safe.
Substitute Sergio Aguero's 97th minute consolation counted for nothing as the pressure piled on manager Ronald Koeman.
However a 2-2 draw in that game meant that Real Sociedad go top by one point, although they have played an extra game than the two Madrid sides.
Luis Suarez scored twice as Atletico recovered from two goals down to get a point. Alexander Soerloth and Alexander Isak had opened up a two-goal advantage for the away side.
Oliver Torres, Rafa Mir, Diego Carlos, Munir El Haddadi and Fernando found the net for Sevilla, while Jose Luis Morales (2) and Gonzalo Melero scored for Levante.
The other match on Sunday saw Real Betis enter the Champions League reckoning by beating Rayo Vallecano 3-2 at home. Alex Moreno, Juanmi and Willian Jose's penalty proved the difference, with Randy Nteka and Alvaro Garcia scoring for Rayo.
Raul Garcia gave the hosts the lead only for Francis Coquelin to equalise just before the hour mark.
In the end, Iker Muniain would emerge as the match winner with a penalty in the 77th minute.
In the fourth and final match of the day, Alaves earned a potentially vital win away at Cadiz.
LA LIGA STATISTICS: