Cameron Norrie and Dan Evans both battled to give Great Britain an unassailable 2-0 lead over France in their Davis Cup tie.
British number one Norrie claimed a gutsy 6-2 7-6 (10-8) win over Arthur Rinderknech to seal the best-of-three tie in Innsbruck, Austria.
Evans had earlier beat Adrian Mannarino 7-5 6-4 in a high-quality encounter.
Joe Salisbury and Neal Skupski will face Nicolas Mahut and Rinderknech later on Saturday.
The tie is Great Britain's first in Group C, with the top teams from each group and the two best runners-up qualifying for the quarter-finals.