Atletico Madrid produced a display of ruthless efficiency to emphatically see of Sevilla at the Ramon Sanchez Pizjuan and close the gap on Barcelona at the top of La Liga to seven points.
Sevilla had lost only once in 16 months at home but they were blown away by the proficiency of the away side's attack.
An exceptional hat-trick from Griezmann and goals from Diego Costa and Koke were scored with relative ease, enough to keep Atletico in the title picture ahead of next weekend's trip to Barcelona.
Sevilla scored two late goals through Pablo Sarabia and Nolito, but they were well beaten by an unusually expansive Atletico.
The hosts began quickly and were almost in front within three minutes. Jesus Navas burst down the right-hand side and picked out Luis Muriel but his effort was kept out by Jan Oblak.
Sevilla continued to probe, though, searching for a way through Atletico's imperious back four. But, for all their dominance in possession, they couldn't find one. Instead, it was the visitors that went in front just before the half-hour mark.
Moments after picking up a yellow card for a typically theatrical altercation with Clement Lenglet, Costa dispossessed Ever Banega and placed the ball past Sergio Rico, wheeling away to celebrate in front of the increasingly riled home supporters. It was, in under a minute, almost an encapsulation of the striker's entire career.
Any momentum Sevilla had built up in the early stages had been sapped by their tenacious visitors. And just before the break, they were two down. Griezmann collected the ball outside the box, glided past three players and picked out the top corner with his right foot to complete a superb individual goal.
Sevilla, in response to having fallen another goal behind, attempted to begin the second half as they did the first. But more defensive laxness proved costly as Costa reached a loose ball in the box before Rico and was brought down by the goalkeeper. Griezmann slotted away the resulting penalty to all but seal an impressive victory with 40 minutes remaining.
The game was threatening to turn into a rout and just after the hour mark Atletico scored a fourth. A woeful back pass from Gabriel Mercado fell to Griezmann, who backheeled the ball into the path of Koke to poke the ball home.
Minutes later, as Sevilla continued to capitulate, Griezmann struck the post. He was in search of a hat-trick, performing at his free-flowing best, and Atletico were rampant. And with 80 minutes played, he had his hat trick, converting Saul's cutback to further enhance the misery of Vincenzo Montella and his players.
There was time for two late consolation goals, however. Sarabia beat the imposing Oblak before Nolito found the net at the near post. But the second half had been a procession and Sevilla, by the end, were glad to leave the pitch.