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|Federer thrashed Bemelmans to move to within two wins of replacing Nadal as world number one. (AFP/Koen Suyk)|
The 36-year-old top seed, a two-time champion at the Dutch indoor event, needs to reach the semi-finals to take back the number one spot from Rafael Nadal.
With two more victories, Federer would become the oldest man by three years to hold the top position in the rankings.
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 on Thursday takes on German Philipp Kohlschreiber, against whom he stands 12-0 in career meetings.
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.
Dimitrov won the opening set against Sugita but fell behind a break in the second before levelling for 5-all.
As the set went into a tie-break, the Bulgarian surged ahead as he took a 5-2 lead but had to hold off his opponent as Sugita clawed back to within a point of levelling.
Dimitrov then sent a forehand into the corner to earn a pair of match points and advanced on his second with a service winner to end the resistance of the 41st-ranked Sugita.
"It was my first match in three weeks, and you're always a little rusty," said Dimitrov who has been dealing with a sore shoulder in recent weeks.
"I was trying to find rhythm. I faced a quality player and I'm happy with how things went for me today - I was pain-free in my shoulder."
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.
Pouille lost in 93 minutes, hitting a dozen aces in defeat but losing serve four times.
The 34th-ranked Rublev owns his only career title from Umag last summer on clay. Herbert will play Russian Daniil Medvedev in the second round.
Robin Haase won an all-Dutch affair over Thiemo de Bakker 6-2, 6-2.