Diego Costa passed up the chance to send the home side into an early lead from the penalty spot, but the striker did convert late in the half to leave Atletico with a one-goal lead at the interval.
Costa moved onto 10 league goals for the season as he completed his brace after 62 minutes, but Nolito had one back for the away side 10 minutes later.
Celta forced the issue in the latter stages, but they could not make the breakthrough as Atletico moved level on points with Barcelona at the top of the division.
Read how it all unfolded in Sports Mole's minute-by-minute live commentary of the action below.
ATLETICO MADRID: Courtois; Juanfran, Miranda, Godin, Luis; Gabi, Suarez, Koke; Turan, Costa, Villa
CELTA VIGO: Yoel; Mallo, Costas, Fontas, Toni; Oubina, Lopez; Rafinha, Augusto, Krohn-Dehli; Charles