The Atletico Madrid shot-stopper produced a remarkable triple-save to deny Julian Brandt and Kevin Volland in the second half of the 0-0 last-16 second-leg draw at the Vicente Calderon.
Oblak, who missed the 4-2 first-leg victory in Germany due to injury, has kept 13 clean sheets this season and a total of 14 in the Champions League since his debut in 2014-15 - a tally only Juventus veteran Gianluigi Buffon can match.
And team-mate Griezmann believes there is no finer player in his position.
"It's why we say he's the best goalkeeper in the world," said the France star. "He proves it in every game and he did so again."
Oblak: "Atleti fans know what an achievement it is to qualify for four consecutive quarter finals. We want to do great things." #UCL pic.twitter.com/F2XQS5kJg5 — Champions League (@ChampionsLeague) March 15, 2017
Leverkusen's Bernd Leno also made some fine saves to deny Angel Correa and Koke, while Griezmann came close to breaking the deadlock with a clever chip that went narrowly wide.
Although he was frustrated not to score, the 25-year-old was delighted to reach the quarter-finals for the fourth season in a row under head coach Diego Simeone.
"We had some chances but we didn't have the luck," he said. "But the most important thing was to reach the quarter-finals and we're already thinking about the next game.
"We didn't plan to attack like crazy and we're in the quarters, so everybody is happy.
"It seems like it's easy but there are a lot of matches and you have to give it everything. We've done that every year.
"If you want to reach the final, you have to beat every team you face."