With more than six overs left, the Netherlands were 92 for two in pursuit of a modest total of 121 for six but lost three wickets for 10 runs to turn the match into a nail-biter.
With six runs required in the final over, man-of-the-match Bas de Leede (30 not out) smashed fast-bowling all-rounder David Wiese over his head for four and struck another two down the ground to claim victory with three balls to spare.
The Netherlands, who edged the United Arab Emirates in a tense opener on Sunday, move into top spot of Group A and will reach the Super 12's if the Emiratis can shock Sri Lanka in the later match on Tuesday.
It was a big let-down for Namibia, however, after their stunning, 55-run demolition of Sri Lanka at the same venue on Sunday.
Namibia won the toss and chose to bat but were down to 3-32 before the end of the powerplay and never recovered despite 43 from all-rounder Jan Frylinck.
