Isner needed 3 hours, 21 minutes and four sets to emerge with a 6-3, 7-6 (7-4), 5-7, 6-3 triumph over Tsonga that handed the Americans an insurmountable 3-1 lead in the best-of-five tie.
With the surprising win, the United States continued an underdog run through this year's Davis Cup competition. The U.S. squad also upended Roger Federer's Swiss team in February and has now won two straight clay-court ties on the road for the first time in 22 years.
The United States, which last claimed the Davis Cup in 2007, will head to Spain for September's Davis Cup semifinals.
The defending champion Spain advanced Sunday with a win over Austria.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys