The 26-year-old told BBC Sport: "It was a strong start for me today. Few chances to break him in the first set.
"I'm just thinking about what I need to do on court - to win every match I play in. I'm dedicated to go far in this tournament.
"I'm playing my best grass-court tennis which is good because it's not my preferred surface."
Djokovic will play Argentina's Juan Martin del Potro in the semi-finals.