The 13th seeded American triumphed in one hour and 49 minutes over the Scot, who entered the event as a wildcard and had beaten lucky loser Noah Rubin in the first round.
Tiafoe won 7-6 (7-4) 6-3, saving three set points in the first set, before winning the tiebreak and taking command in the second.
Murray sent down 10 aces across the match but struggled on his second serve and on return.
"The positive thing is that I moved well and served well but my level is up and down with no real consistency," Murray said after the match in North Carolina.
"There are moments in matches where I play well and then I make mistakes or miss returns. I wish I wasn't doing that.
"My level is around 50 or 60 in the world. It's frustrating because if wasn't moving great and not feeling good physically then I would be a bit easier on myself. But when I'm winning a low percentage of second-serve points, that's got nothing to do with the physical side of things."
Sixth seed Marin Cilic also bowed out, losing 4-6 7-5 6-4 to Belarussian Ilya Ivashka, who sent down 16-13 aces.
Fifth seed Alexander Bublik was also bundled out, going down 6-2 7-6 (7-5) to Finland's Emil Ruusuvuori.
Top seed Pablo Carreno Busta dropped a set but edged past Kwon Soon-Woo 6-3 3-6 6-4.
British third seed Dan Evans came from behind to beat Lucas Pouille, while fourth seed Marton Fucsovics won in straight sets over Yosuke Watanuki.