The top-seeded Swiss did not face a break point on serve during the one-hour match, as he improved to a 15-0 FedEx ATP Head2Head record against the 33-year-old Finn.
"I'm happy that I won my first match ever in Turkey," he said. "In the second set Jarkko started playing better and I'm happy that I managed to close the match."
Federer, who is looking to win his 11th clay-court title this week, will face Daniel Gimeno-Traver in the quarter-finals, but first, he planned on making good use of his day off Thursday.
"Tomorrow I have a day off and I will enjoy and do a sightseeing trip by boat on the Bosphorus to see some more of this beautiful city," he said.
Earlier Wednesday, Gimeno-Traver fired five aces past sixth seed Mikhail Kukushkin in a 6-3, 6-3 win, his third in four meetings against the Kazakh. The in-form Spaniard is 7-2 in his past two tournaments, highlighted by a runner-up finish at the Grand Prix Hassan II (l. to Klizan).
Fourth seed Santiago Giraldo booked a spot in his third ATP World Tour quarter-final of the year with a 6-4, 1-6, 6-3 over last year’s junior World No. 1 Andrey Rublev.
Meanwhile, eighth seed Diego Schwartzman swept past Jurgen Melzer 6-0, 6-2 in 52 minutes.