The 36-year-old top seed, a two-time champion at the Dutch indoor ABN AMRO event, needs to reach the semi-finals to take back the number one spot from Spaniard Rafael Nadal.
"It's very surprising how good things went today," Federer said. "The key is to start well, put him under pressure.
"I wanted to make him think he had to do something special to beat me. I did well there, I felt good, I'm healthy and I'm confident. It was a great first round for me."
Federer gave no quarter as he raced to a 5-0 lead, with the out-matched Bemelmans winning his first game after 16 minutes.
The outcome was never in doubt as Federer dominated with six aces and four service breaks, winning an impressive 21 of 23 first-serve points in the demolition.
The 20-time Grand Slam champion takes on German Philipp Kohlschreiber, against whom he stands 12-0 in career meetings.
"You always prefer to play the guy whose game you know," Federer said.
"You know his patterns, it's nice to play someone like that, you know what to expect.
"My start will be crucial, I need to stay focused all the way. Any lapses can get you into trouble."
Third seed Alexander Zverev fell in an upset to qualifying lucky loser Andreas Seppi of Italy, 6-4, 6-3 in the second round to open up Federer's half of the draw.
Grigor Dimitrov and David Goffin, the duo who faced off in last year's season-ending ATP Finals, both advanced with straight-sets wins.
Second seed Dimitrov, who beat Belgian fourth seed Goffin in the London final last November, had to fight back in the second set to defeat Japan's Yuichi Sugita 6-4, 7-6 (7/5) in their first-round encounter.
Goffin made light work of veteran Spaniard Feliciano Lopez, cruising through 6-1, 6-3 to reach the quarter-finals.
Last weekend's Montpellier champion Lucas Pouille exited in his opening match, losing 7-5, 6-4 to Andrey Rublev.
The Russian was joined in the second round at the Ahoy Arena by Pierre-Hugues Herbert of France, who advanced after just 15 minutes when compatriot Richard Gasquet, the Montpellier finalist, retired with a groin injury trailing 3-1.
Robin Haase won an all-Dutch affair over Thiemo de Bakker 6-2, 6-2.