The four-time champion created 21 breakpoints against debutant Koepfer on his way to recording his 29th victory in 30 matches this year.
The 17 time Grand Slam champion has now reached the last eight in Rome each year since 2007 and has now won seven straight quarter-final matches at the ATP Masters 1000 event, dating back to his loss to Tomas Berdych at this stage in 2013.
Djokovic who ties Rafa Nadal on 35 Masters is now two wins shy from lifting a record-breaking 36th Masters 1000 crown.
Watch the highlights of Saturday’s matches below
Koepfer, who was making his debut in the main draw at a Masters 1000 event this week saved one match point to earn his first ATP Tour victory on clay against Alex de Minaur and clinched his first Top 10 victory against Gael Monfils in the second round.
Koepfer becomes the first qualifier to reach the quarter-finals at this event since Juan Monaco and Mischa Zverev in 2009.
“[Dominik] has a good pop on the serve, so you have to guess,” said Djokovic. “
“He steps in when he is feeling the ball, he steps in on both the forehand and backhand and moves well. I think his game is really ideal for this surface and him reaching the quarter-finals proves he is in good form.”
Djokovic will face Casper Ruud in his match. The Norwegian beat fourth seed Matteo Berrettini 4-6, 6-3, 7-6(5) in just under three hours to reach his first Masters 1000 semi-final.