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.
