Celta substitute Manuel “Nolito” Agudo halved the deficit in the 71st and the forward threatened to grab the equalizer late, but a tiring Atletico held on to the three points.
While Simeone and his players insist they are not contemplating a challenge for the league title with their mantra of “just going forward game by game,” Celta coach Luis Enrique is one of many who considers them a contender.
“It's not for me to talk about them, but they are the most dangerous opponent we have faced so far,” said Enrique. “If they keep playing at this level it would be silly not to consider them for the title.”
Later, Valencia visits Athletic Bilbao, Sevilla hosts Almeria, and Real Betis plays at Getafe.
While Diego Costa continued to impress, his strike partner David Villa had a game he will likely want to forget.
Celta goalkeeper Yoel Rodriguez turned back a number of his shots before Villa wasted a Diego Costa pass that had left him alone with only the goalkeeper to beat. Villa apparently had picked up an injury just before the miss and immediately asked to be substituted in the 58th.
Atletico also lost captain Gabi Fernandez to a left knee injury late, leading to the debut of French midfielder Joshua Guilavogui.
Atletico dominated the first half against a toothless Celta side that couldn't muster a shot on goal and only stayed in the game thanks to Rodriguez's series of fine saves.
Rodriguez was particularly outstanding in the 25th when he blocked two clear chances following teammate Hugo Mallo's foul of Filipe Luis in the area.
Diego Costa stepped up to take the resulting penalty, but Rodriguez smothered his shot and was quick enough to retreat to his far post to push Villa's attempt to poke in the rebound past his post.
But Rodriguez could do nothing when Celta's Alex Lopez knocked the ball back into his own area where Filipe Luis squared for both Diego Godin and Diego Costa to tap the ball in. The goal was awarded to Diego Costa.
Diego Costa's second goal came when he neatly chested down a long pass, used one arm to brush off last defender David Costas, and fired the ball under Rodriguez.
Enrique sent on Nolito and his team finally responded after Nolito pulled one back by chipping the ball over goalkeeper Thibaut Courtois.
Nolito continued to cause Atletico problems until the final whistle, drawing a save from Courtois with a free kick in injury time.
Both Atletico and Barcelona can match Madrid's record start of nine straight wins to start the season in 1968 in the next round after the international break.
