The conditions in Vigo made it difficult for either side to play with real quality for long spells, but second-half goals from Antoine Griezmann and Yannick Ferreira Carrasco ensured that Diego Simeone's side recorded all the points and moved two points clear at the top of the division.
Celta, meanwhile, remain fifth in the table, but they have now lost their last three in the league without scoring and trail fourth-placed Villarreal by eight points.
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It was the visitors that had a half-chance inside the opening three minutes, but Luciano Vietto, who had met a cross from Saul Niguez, could only drop his header over Sergio Alvarez's crossbar. Moments later, Alvarez was called into action to race out of his goal and meet a charging Griezmann, who had controlled a difficult through-ball.
The through-pass behind Celta's back four proved a popular choice for Atletico in the opening 15 minutes and on two separate occasions, Griezmann, who was playing through the middle, almost beat Alvarez to the ball.
Iago Aspas had Celta's first real chance in the 22nd minute, but his header from a Fabian Orellana cross was wide of the post, before Jose Gimenez struck a wild effort wide of the post down the other end.
Koke found space outside the Celta box just past the 30-minute mark, but his effort was wide during a period where both teams were struggling to find that elusive pass on a wet and bobbly pitch.
The clearest chance of an untidy first period came in the 34th minute when Griezmann combined with Koke just inside the Celta box, but the Frenchman fired high of the crossbar with just the goalkeeper to beat.
Griezmann made no such mistake early in the second period, however, as he tapped home from close range after initially finding Vietto with a clever pass in a wide position.
Carrasco, who replaced former Celta midfielder Augusto Fernandez, came close to a second for the visitors just past the hour, but his strike from distance fizzed wide of the post.
Carrasco had his goal in the 80th minute, however, when he showed excellent skill outside the box before firing his effort into the back of the net to make sure that all of the points were returning to the capital.
Both managers made changes late on, but the pattern of the match remained the same as Atletico, who have still only conceded eight league goals this season, recorded yet another three points to move ahead of Barcelona.