Novak will be making his debut appearance at the ATP World Tour 250 grass-court tournament at Devonshire Park.
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).