Roger Federer and Stanislas Wawrinka, who were doubles gold medallists at the 2008 Olympic Games, both won their singles on Friday to give the Swiss a 2-0 lead.
The Netherlands stayed in contention in Amsterdam when Robin Haase and Jean-Julien Rojer stunned Federer and Wawrinka 6-4, 6-2, 5-7, 6-3.
But Federer seal the win when he beat Robin Haase 6-1, 6-4, 6-4 to give Switzerland an unassailable 3-1 lead.
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The Dutch scored a consolation point when Thiemo de Bakker beat Marco Chiudinelli 6-2, 7-6 (7/5) in the final match-up.