Mario Mandzukic opened the scoring before the France attacker killed off the game in the first half to send Atleti three points adrift of Luis Enrique's side
Mario Mandzukic scored an early penalty before teeing up two first-half goals for strike partner Griezmann, as Diego Simeone's side cruised past their struggling visitors - although they played the last few minutes with 10 men after Guilherme Siqueira was sent off for a second booking late on.
It was still a welcome win for the champions, who currently sit third behind rivals Real Madrid and Barcelona having lost to Celta Vigo last time out.
They face Bayer Leverkusen in the Champions League last 16 on Wednesday before back-to-back meetings with fellow top-four contenders Sevilla and Valencia.
The home side's intentions were clear from the outset, but the breakthrough came with the help of a contentious spot-kick.
Mandzukic and Griezmann demonstrated their developing partnership for the next two goals to put the result beyond doubt before half-time, allowing Simeone to rotate his squad after the break.
Almeria, meanwhile, saw their three-match unbeaten run end, meaning results on Sunday could drag them closer to the drop zone.
Simeone's side started the match with plenty of purpose and intensity to their play and got their reward in the 13th minute, albeit in controversial circumstances.
Diego Godin was adjudged to have been fouled in the penalty area while attempting to meet Gabi's floated free kick.
Mauro Dos Santos was identified as the chief offender, although he and his team-mates, two of whom also jumped with the Uruguayan, looked bemused at the penalty award.
Mandzukic ignored all of the arguments to coolly convert the spot-kick and give Atleti the lead.
Things got worse for the visitors in the 20th minute, and this time there were few doubts about the main culprit.
Fran Velez inexplicably played the ball to the feet of Mandzukic 40 yards from goal and the former Bayern Munich frontman was able to send his strike partner Griezmann through to double the lead with a composed finish.
The game was all-but over as a contest nine minutes later when Griezmann and Mandzukic combined once again to add a third goal.
The Frenchman managed to get the wrong side of his defender inside the six-yard box to latch on to Mandzukic's knockdown and fire past Julian on the turn, as Almeria failed to deal with another aerial ball.
Almeria did their best to respond in the opening minutes of the second half and did increase their tempo, but Atleti managed to maintain their superiority.
With one eye clearly on their return to European action, Simeone was able to withdraw Mandzukic and Griezmann to standing ovations in the second period, to be replaced by Fernando Torres and Raul Garcia.
Garcia almost marked his return from suspension with a goal, but he dragged his shot across goal from six yards out, after a strong surge into the box in the 77th minute.
That was as close as either side came to adding a second-half goal, and the only blot on otherwise fantastic outing for Atleti was the late sending off for Siqueira.
The defender was shown a second yellow card for deliberate handball on the half-way line, but it mattered little to the overall context of the match.