Meanwhile, Gary Neville's winless streak in the league since taking charge of Valencia last month stretched to five games as Jonathas's late double handed Real Sociedad a 2-0 victory.
Griezmann slotted home his 14th goal of the season after a wonderful one-two with Luciano Vietto before Carrasco's deflected effort sealed a ninth La Liga win in Atletico's last 10 games.
Victory moves Diego Simeone's men two points clear of Barcelona - having played a game more - at the halfway stage of the season and maintains their four-point advantage over Real Madrid.
Simeone demands more from table-topping Atletico
"We were strong at the back and we know up front when we have chances we can score goals at any moment," Griezmann told Canal Plus.
"I always say the best is yet to come. I am working to be an important player and hopefully I can continue in the same vein."
Torrential rain in recent days in Vigo had threatened to force the game to be postponed, but Atletico handled the difficult conditions better to inflict Celta's third consecutive league defeat.
Griezmann fired a warning shot just before the break with a rasping drive that flew inches over the bar.
La Liga: Atletico up to second with Betis win
However, it was a rare piece of quality of football that opened the scoring four minutes after half-time as Griezmann started the move before being picked out by Vietto to tap in at the back post.
For the fourth game in a row Simeone's substitutions then bore fruit as Jackson Martinez's presence allowed Carrasco to drive into the box before smashing the ball past Sergio Alvarez.
Earlier, Valencia slipped 16 points off the top four in 11th after defeat to a rejuvenated Real Sociedad since David Moyes's sacking in November.
Neville's men had shown promising signs in holding Real Madrid 2-2 last weekend and a 4-0 thrashing of Granada in the Copa del Rey in midweek, but have now gone two months without a league win to almost certainly end their hopes of reaching the Champions League next season.
"It's a blow, we needed momentum, but we played well below the expectations we have set ourselves," said Neville.
"We have to snap out of it and start winning. I can only ask the fans to be patient. The dressing room is disappointed, as am I, but tomorrow is a fresh start and we have to get the fans to believe."
Valencia 'keeper Jaume Domenech had kept his side in the game for long spells after both sides has hit the woodwork early on.
However, he was at fault when he flapped at Carlos Martinez's deflected cross and Jonathas bundled home from close range 12 minutes from time.
The same two players combined for the second four minutes later as the Brazilian this time thumped home the full-back's cross with a bullet header into the bottom corner.
Villarreal strengthened their hold on fourth as Cedric Bakambu struck twice to remain just five points off Atletico with their sixth successive La Liga win.
Former Tottenham Hotspur striker Roberto Soldado provided the ammunition for both his strike partner's goals with crosses that Bakambu clinically dispatched either side of half-time to take his tally for the season to 12.
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