The 33-year-old Scotsman advanced in hot and humid conditions to a second-round date with German fifth seed Alexander Zverev at the Covid-19 quarantine bubble that will also be used for the US Open, which starts on Aug 31.
Murray won the 2012 US Open as well as the 2013 and 2016 Wimbledon titles plus the 2012 and 2016 Olympic gold medals.
Former world number one Murray, now ranked 129th, suffered a pelvic injury at Davis Cup last November and that, combined with the pandemic shutdown, kept him out of competition until he faced 22-year-old Tiafoe in a meeting of wildcard entrants.
Murray broke Tiafoe for a 2-0 lead in the third set when the American missed a volley, broke again to 5-1 with a backhand return winner and held at love to finish matters after two hours and 28 minutes.
Murray was the 2008 and 2011 winner in this Grand Slam tuneup event, usually staged in Cincinnati but moved to New York due to the Covid-19 pandemic that wiped out much of the season, including Wimbledon.
Tiafoe, ranked 81st, forced the only break point of the first set in the 11th game with a lob winner but Murray dismissed it with a service winner up the middle and held to 6-5 on a second-serve ace.
In the tie-breaker, Tiafoe jumped ahead 5-2 before Murray roared back, saving a set point to reach 6-6 when Tiafoe sent a backhand wide and taking the set two points later on a passing forehand winner.
Tiafoe, whose only ATP title came at the 2018 Delray Beach Open, saved a break point with an ace in the fifth game of the second set and took the first break of the match for a 5-3 lead on a backhand drop volley winner before holding to force a third set.
The match was played on the National Tennis Centre Grandstand court, the event’s feature court with no matches until the US Open scheduled at Arthur Ashe Stadium or Louis Armstrong Stadium.
On the women’s side, Greek 13th seed Maria Sakkari defeated US teen Coco Gauff 6-1, 6-3 in 64 minutes. Sakkari could face 23-time Grand Slam winner Serena Williams in the third round.
Russia’s Ekaterina Alexandrova ousted Kazak ninth seed Elena Rybakina 7-5, 7-6 (8/6).
Among those set to play later were seven-time Grand Slam champion Venus Williams and 2014 US Open winner Marin Cilic of Croatia.