Atletico and Valencia join holders and record winners Barcelona, Athletic Bilbao, Sevilla, Celta Vigo, Las Palmas and second-division Mirandes, the only non-La Liga side left in the competition, in Friday's draw for the last eight.
Rayo held their more illustrious city neighbours to a 1-1 draw in last week's last 16, first leg at their Vallecas stadium and were sniffing a possible upset ahead of the return across town at Atletico's Calderon arena.
Angel Correa's powerful strike from the edge of the penalty area, which flew in off the underside of the crossbar, put the 2013 winners ahead five minutes before halftime.
Griezmann hooked in a second for the home side in the 80th minute and the in-form France forward made it 3-0 in added time with a breakaway goal for a 4-1 aggregate victory.
Rayo, who are second from bottom in La Liga at the halfway stage, barely troubled Miguel Angel Moya in the Atletico goal and must now turn their attention to avoiding relegation.
Valencia coach Gary Neville rested several regulars for the visit to Granada after a thumping 4-0 victory in the first leg at the Mestalla.
Granada, also struggling in La Liga, had the better of the early exchanges and Ruben Rochina's first-time shot came back off the inside of a post in the 21st minute.
However, midfielder Wilfried Zahibo made the most of an error by goalkeeper Ivan Kelava and headed in at a corner in the 42nd minute to snuff out any hopes of an unlikely Granada comeback.
Paco Alcacer sped clear to score in the 63rd minute moments after coming on to replace Alvaro Negredo and Pablo Piatti completed the scoring and a 7-0 aggregate success with a penalty six minutes from time.
"Granada were excellent in the opening minutes," Neville, who took over from the sacked Nuno Espirito Santo last month, told a news conference.
"But as the game went on I think we were the better team," added the former Manchester United and England defender.
The quarter-finals will be played over two legs later this month, with the semi-finals at the start of February and the final on May 21.
(Reporting by Iain Rogers, editing by Toby Davis)
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