The Austrian sixth seed beat the defending champion in straight sets 7-6 (5), 6-3, 6-0 in two hours and 15 minutes.
Novak continued his good run on Parisian clay as he defeated Albert Ramos-Vinolas 7-6 (5), 6-1, 6-3 to reach the last 8.
The second seed moved into the French Open R4 for the 11th time with a five-set win over Diego Schwartzman.
Novak won his first French Open title in 2016 and completed career Grand Slam beating Andy Murray in the final (3-6, 6-1, 6-2, 6-4).
With a 6-3, 6-1, 6-4 victory over 13th seed Dominic Thiem, Nole is one match win away from completing a career Grand Slam.
Novak cruised into his 30th Major semi-final with a 6-3, 7-5, 6-3 victory over no.7 seed Tomas Berdych on Thursday.
The Serbian ace is in the final eight at a Grand Slam for the 28th consecutive time, surpassing Jimmy Connors for second best streak ever.
No.1 seed defeated world no.66 Aljaz Bedene 6-2, 6-3, 6-3 to reach the last 16 of Roland Garros.