Having seen top seed and two-time champion David Ferrer withdraw due to illness, Granollers will have fancied his chances of threatening the latter stages.
However, the fourth seed threw away a one-set lead against the German at the ATP 250 grass-court event to bow out at the first hurdle.
Granollers came from two games down early on to move ahead before Becker reeled off the final three games of the second set to draw level.
Becker won all but two of his first service points in the decisive set to progress 4-6 6-3 6-4.
Dmitry Tursunov avoided the same fate as Granollers, though, the fifth seed only enduring difficulties late in the second set of his 6-3 7-6 (7-3) win over Bradley Klahn.
The Russian looked on course for a more comfortable route to round two when he broke to move 5-3 up in the second set.
Klahn, however, hit back to force the tie-break, but Tursonov's superior quality and experience shone through as he took his third match point.
Sixth seed Vasek Pospisil was made to work hard for his 6-4 7-5 victory over Serbia's Dusan Lajovic in his first outing in s-Hertogenbosch.
The Canadian world number 35 got the crucial break in each set before progressing, with Lukas Rosol or Jan-Lennard Struff next up.
Slovak qualifier Lukas Lacko overcame Romania's Victor Hanescu 6-3 6-4 to book a second-round place, while Steve Johnson - fresh from his quarter-final run in Halle last week - was too strong for France's Kenny De Schepper (7-6 (7-3) 7-5).
Elsewhere, Thiemo De Bakker won his all-Dutch affair against Igor Sijsling 6-4 7-6 (7-4) and Matthew Ebden held off a fightback from Adrian Mannarino to clinch the first meeting between the pair 6-3 4-6 6-3.
Ebden will face Spanish opposition in the next round in the form of Daniel Gimeno-Traver or third seed Roberto Bautista Agut, who meet on Tuesday.