Murray dismissed Querrey 7-6 (7-5), 6-7 (3-7), 6-1, 6-3 in the first reverse singles match at Petco Park in San Diego, giving Britain an insurmountable 3-1 lead in the best-of-five opening-round series.
The reigning Wimbledon champion wrapped up Britain's first victory over the United States in Davis Cup competition since 1935.
Murray had given his country a 1-0 lead with Friday's opening win over Donald Young and James Ward doubled Britain's advantage with a triumph over Querrey.
Bob and Mike Bryan kept the Americans alive Saturday with doubles decision over Colin Fleming and Dominic Inglot.
Britain now goes on to face Italy in April's quarterfinals.