Monfils registered the only win of the final for France when he triumphed 6-1 6-4 6-3 over world number two Roger Federer in the second singles encounter.
The victory levelled the final at 1-1, but Switzerland's success in the doubles, followed by a 6-4 6-2 6-2 win for Federer against Richard Gasquet, gave them an unassailable lead.
Monfils' climb is the only change in the world's top 20, with Novak Djokovic ending the year as number one ahead of Federer and Rafael Nadal.
Elsewhere in the top 100, Diego Schwartzman moved up 16 places to 61st, while Ricardas Berankis climbed from to 86th from 107th.
Also breaking into top 100 is Go Soeda - up 17 places from 117th.