The Swiss maestro needs to reach the semi-finals to go back to number one, having won the tournament twice, and needed just 47 minutes to end qualifier Bemelmans' challenge.
Federer, the 20-time grand slam champion, raced through the first set in a little over 20 minutes and found precious little resistance in the second.
The evergreen 36 year-old – back in competitive action for the first time since winning his sixth Australian Open title – was quickly into his stride, breaking his opponent at the first opportunity as his finesse and precision came to the fore.
World number 116 Bemelmans, facing Federer for the first time, simply could not live with the veteran's stunning array of shots.
And Federer's tactical nous was also evident, moving Bemelmans around the court at will and exploiting the gaps off both wings.
When Bemelmans could get a look-in, his rare winners were met with warm applause from a sympathetic crowd.
But the overawed 30 year-old was merely delaying the inevitable and Federer can surely expect a sterner test from second-round opponent Philipp Kohlschreiber.
It is a tough field in Netherlands, even after the shock exit of Federer's compatriot Stan Wawrinka, with Grigor Dimitrov and David Goffin in particular providing stiff competition.
Second seed Dimitrov, who reached two grand slam semi-finals last year, overcame Yuichi Sugita 6-4 7-6 (7-5).
Goffin, seeded fourth and runner-up in 2017, was even more impressive in his 6-1 6-3 success over Feliciano Lopez.
The Belgian faces Tomas Berdych next, the sixth seed having beaten Viktor Troicki 6-1 6-2.
But Zverev, playing in the last match on court, was downed by Andreas Seppi 6-4 6-3.
With the big names back-loaded in the schedule, the earlier matches set the tone of one-sided encounters.
None of the ties went the distance and, indeed, the first one up ended after four games, with Richard Gasquet retiring hurt when 3-1 down against French compatriot Pierre-Hugues Herbert.
Elsewhere in the draw, there were wins for Robin Haase, Andrey Rublev – who surprised seventh seed Lucas Pouille – and Damir Dzumhur.