Diego Simeone's men crashed out of the Copa after a 3-2 home defeat by Barcelona on Wednesday and they were greeted with torrential rain in the Basque Country – initially plunging the game into doubt - but the Liga champions produced an instant response as they cruised in testing circumstances.
Eighth-placed Eibar rarely looked capable of causing a splash on Saturday, with Griezmann's eighth league goal from his last six outings giving Atletico a seventh-minute lead.
The France international was then the architect for Atletico's second, crossing for the equally sharp Mario Mandzukic to prod home.
Mandzukic added his 10th Liga goal of the season in the 27th minute and, sensing the match was already won, a stubborn Atletico sat back and tightened their grip thereafter.
Eibar improved after the break, though Federico Piovaccari's consolation goal came a minute from time and did little to change the outcome as Atletico remain four points off the pace of rivals Real Madrid in the Liga title race.
Despite the saturated pitch, Atletico did not resort to a direct style of play and their commitment to playing the ball was rewarded after just seven minutes.
Griezmann peeled away to the left and was played into the area by Raul Garcia, the French attacker slamming a precise effort into the bottom-right corner.
Eibar were not quite so keen to stick to the principles of short passing, though, often pumping the ball into the box to give Miguel Angel Moya something of a physical test.
But the goalkeeper was more than a match and Atletico made the most of Eibar's lack of ingenuity, as Mandzukic steered a left-wing delivery in from close range after 23 minutes - Griezmann turning provider this time.
And Eibar again failed to cope with the Croatian four minutes later.
Abraham and Raul Navas hesitated in defence, leaving Mandzukic room to blast past a helpless Xabi Irureta in Eibar's goal.
The hosts were finally presented with their first chance in the 43rd minute, but Piovaccari fired straight at Moya after Diego Godin's clearance struck Tiago and fell kindly for the Italian.
Eibar attempted to up the ante at the start of the second half, passing the ball around quicker in the marginally improved conditions.
But they continued to struggle crafting opportunities, with Mikel Arruabarena's tame half-volley in the 52nd minute about as much as they could muster, leaving Moya largely untroubled.
Atletico showed little determination to add a fourth in a second half which failed to ignite much excitement and, although Piovaccari headed in Saul Berjon's cross at the end, Simeone's side strode to a routine triumph.
