Berdych won his third match of the best-of-five series with a 6-1, 6-4, 6-3 win in the decisive rubber singles match in Ostrava to clinch a berth in the April series against Japan.
Igor Sjisling of the Netherlands knocked off Lukas Rosol in the final match of the day to close out the series 3-2.
Berdych broke De Bakker's serve six times Sunday and hit 93 winners out of the 157 points played.
De Bakker had beaten Berdych on the pro tour last year, but was no match for the Australian Open semi-finalist on Sunday.
Celebrity Families of 2014 [PHOTOS]