The France international was in lethal form for the champions, scoring twice in the first half and playing a pivotal role in the third - an own goal - as Atletico eased to a routine triumph at the Vicente Calderon on Saturday.
Griezmann pounced on a defensive mistake to break the deadlock in the 12th minute and doubled his tally midway through the opening half.
Rayo lost the corresponding fixture 5-0 last term and, although Roberto Trashorras netted to halve the deficit with 35 minutes gone, Paco Jemez's men rarely looked capable of gaining revenge.
Griezmann's search for a hat-trick proved fruitless, but he did play an integral part as Atletico re-established a two-goal lead in the 56th minute, crossing for a Manucho to put through his own net.
Diego Simeone's men seemed to ease off the throttle towards the end, but the result was secured and they stay four points behind pacesetters Real Madrid.
Atletico put Rayo under pressure right from the start and the visitors almost contributed to their own downfall in the sixth minute, but Ze Castro cut out Arda Turan's teasing delivery after a dreadful pass by goalkeeper Tono.
The former Atletico defender turned culprit six minutes later, though, as Ze Castro saw his pass intercepted by Griezmann, who burst free and coolly slotted beyond Tono.
And the France international doubled his tally with 22 minutes on the clock, prodding past the goalkeeper after being released on goal by a Mario Mandzukic header.
Despite offering very little attacking threat, Rayo pulled one back 10 minutes before the break, as Trashorras steered home from the edge of the area after Gael Kakuta showed great awareness to pick out his captain.
Atletico began the second half brightly and Griezmann almost completed his hat-trick in the 51st minute, but Tono managed to keep the Frenchman's miscued cross out with a desperate dive to his right.
The goalkeeper was rendered helpless when Atletico eventually restored the two-goal cushion five minutes later, however, as Manucho knocked Griezmann's corner delivery into his own net.
The Rayo defence simply had no answer to the terrific Griezmann, but a third goal continued to elude him as he fired agonisingly wide of the bottom-right corner just a few moments after the own goal.
Rayo crafted a great opportunity to ensure a tense finish as Alberto Bueno raced on to Trashorras' clever delivery, but he failed to make a proper connection and there was still time for the industrious Griezmann to strike the post.
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