Diego Simeone's side have won seven consecutive games. Atletico trail league leaders Barcelona by two points after the Catalans fell to a shock 2-1 defeat at home against Las Palmas.
Clement Lenglet opened the scoring after 25 minutes and Julian Alvarez added the second. Rodrigo de Paul swept home the third before half-time and Griezmann produced a wonderful turn and finish soon after the break to add the fourth on a memorable night for the Rojiblancos, which even some home fans applauded.
Alexander Sorloth wrapped up Atletico's thumping victory in stoppage time. "I have to thank (the Valladolid fans), in the end, it's what all players want, we want people to enjoy it with us, whether it's opposition or our own fans," Griezmann told DAZN. "In the end, I have to be grateful for this love, I'm doing really well and I hope to give more."