Diego Simeone's side failed to register a shot on target in their 0-0 draw with Villarreal before the international break, which followed a similarly dismal performance in a goalless meeting with Huesca.
Suarez settled any nerves early on at the Balaidos, though, scoring his third Atleti goal in the sixth minute to become the second fastest player to reach a 150 in LaLiga in the 21st century after Cristiano Ronaldo.
Atleti confirmed a 200th LaLiga win under Simeone late on when Carrasco headed home after Joao Felix's effort crashed back off the crossbar.
The visitors started with a spring in their step and Suarez's shot from 12 yards squirmed underneath Ivan Villar after the Uruguayan was picked out by Manuel Sanchez following a slick move down the left.
The hosts carved out two clear opportunities to level midway through the first half. Sergio Carreira crashed an effort against the upright after stealing in unmarked at the back post, before a clean-through Santi Mina was denied by Jan Oblak's outstretched foot.
Thomas Lemar saw his corner bounce back off the crossbar with Villar flailing, but another goal for Atleti before the break would have been harsh on Celta, who ended the first half with 10 attempts on goal to the visitors' three.
Suarez was denied a second immediately after the restart as Villar diverted his close-range effort from Diego Costa's pass over the crossbar.
Atleti looked far more robust at the back in the second half, limiting Celta to a series of half-chances, while at the other end Villar got down well to push substitute Marcos Llorente's low strike past the post with 15 minutes remaining.
The visitors' jump to fourth in the table was sealed in the fifth minute of stoppage time when substitute Carrasco headed past Villar after sublime skill from Joao Felix had resulted in his powerful strike rebounding off the crossbar and into his path.
What does it mean? Atleti bounce back with trademark win
It was rarely pretty but Simeone will hardly care as he became the second head coach to win 200 LaLiga games a single club – former Real Madrid boss Miguel Munoz (257) is the only man with more. Like so many of those wins, the three points did not come easily for Atleti. They were indebted to a combination of wasteful finishing from Celta and typically robust goalkeeping from Oblak to claim a second win of the campaign.
Torreira wastes little time making his mark
Making his first start since a loan move from Arsenal earlier this month, Lucas Torreira was an industrious presence at the heart of Atleti's midfield. The Uruguay international gained possession six times - a team high alongside Stefan Savic - and led the way for interceptions with five.
Costa labours before early departure
Aside from one incisive pass to Suarez, Costa looked a shadow of his former self. He managed only one shot on goal and made just 12 passes before he hobbled off injured in the 50th minute.
Key Opta facts
- Simeone recorded his 200th win in his 330th game for Atletico in LaLiga, making him the second coach to reach the milestone for the same club in the competition, after Miguel Munoz (257).
- Atletico are unbeaten in their last 20 LaLiga games (W11 D9), equalling their best unbeaten streak in the competition (20 in 2017, W13 D7).
- Lucas Torreira completed 53 passes in his first game for his new team (59 total passes), more than any other Atleti player on their LaLiga debut since at least 2005-06.
- Celta Vigo have lost 63 of their 105 games against Atletico in LaLiga (W23 D19) - that is more than any other opponent in LaLiga.
- Suarez is the first player to score three or more goals in his first four appearances for Atleti in LaLiga since Radamel Falcao in 2011 (five goals).
Atleti start their Champions League campaign with a trip to holders Bayern Munich in Group A on Wednesday, before hosting Real Betis in LaLiga three days later. Celta, meanwhile, travel to Levante in the league on October 26.