It took Diego Simeone's side less than one minute to find the opening goal when Alvaro Morata tapped in from Angel Correa's low cross after 52 seconds.
No other Atletico player has scored more goals than the Spaniard's four since the return of LaLiga Santander.
Brais Mendez was arguably Celta's brightest spark in the first half and he came closest to beating Jan Oblak with a shot that flashed wide a few minutes before the break.
It was Mendez who created the hosts' equaliser shortly after half time when he sent a cross towards Fran Beltran in the penalty area.
Whether it was intentional or not, Beltran's instinctive volley flew off his boot and looped over Oblak, into the back of the net.
The draw takes Los Rojiblancos nine points clear of fifth-place Getafe as they edge closer to Champions League qualification.
Oscar Garcia's Celta, meanwhile, take another step towards survival in LaLiga Santander, moving six points clear of the relegation zone.