Griezmann's 20-yard free-kick crashed in off the underside of the crossbar to clinch an important victory that closes the gap to third-placed Sevilla to just two points, with Jorge Sampaoli's side in danger of falling 11 points adrift of leaders Real Madrid, who have a game in hand.
The France international's effort added to a first-half header from Diego Godin as Atletico followed up booking a place in the Champions League quarter-finals by completing a 4-2 aggregate victory over Bayer Leverkusen last week with a third straight top-flight win.
For Sevilla, though, it was a case of their late-season stutter continuing. The Andalusian side were sent crashing out of Europe by Leicester City and are now winless in four outings in all competitions - a run that has seen their focus turn to the teams below them rather than above.
A change of formation for the second half was not enough to inspire a comeback from Sevilla, who fell three goals down when Koke rounded off a swift break with a finish into an empty net.
Substitute Joaquin Correa struck a consolation for Sevilla five minutes from time, but it was not enough to stop their season-best seven-match unbeaten run in the top flight from ending.
Diego Simeone welcomed Gabi and Kevin Gameiro back from their respective injuries but lost Sime Vrsaljko to a knee problem inside just two minutes, Juanfran replacing him.
Atletico did not dwell on that early blow and nearly took the lead through Gameiro in the 13th minute. He was released by Yannick Carrasco and his attempt to chip Rico from the right-hand side of the box struck the bar after brushing the goalkeeper's fingertips.
The hosts controlled the early possession but Sevilla gradually gained more of a foothold in the match and could have had a penalty in the 34th minute when Wissam Ben Yedder went down under a challenge from Jan Oblak – though replays showed contact between the two was minimal.
Atletico heeded the warning and Godin got away from Gabriel Mercado to turn Griezmann's header beyond Rico, sending them into half-time with the advantage.
Sampaoli changed from a three-man defence to a back four for by replacing Clement Lenglet with Stevan Jovetic, and Atletico began to find extra space in their defence.
Griezmann was unable to take advantage of the first chance that came his way in the 50th minute, stabbing wide after neat interplay with Gameiro put him one-on-one with Rico.
However, he did not make the same mistake with his next opportunity. Mercado's foul on Gameiro gave Atletico a free-kick that Griezmann fired home sweetly from just outside the area.
Fernando Torres came on for his first appearance since sustaining a head injury in the 1-1 draw with Deportivo La Coruna on March 2, but it was Koke who struck next for Atletico with a tap in after a counter-attack.
Correa had replaced Ben Yedder in the 64th minute and he guided a cool finish beyond Oblak, though it was not enough to stop Atletico claiming a superior head-to-head record that could prove crucial come the end of the season.