Belgian qualifier Goffin ousted Melzer 6-3 6-4 in their first-round affair at the ATP 250 event in North Carolina - the last hard-court warm-up event for the US Open, starting Monday.
Only six of Goffin's streak wins have come at ATP World Tour level, with the run including Challenger Tour events and qualifying but his formline is nonetheless imposing heading towards the year's final major.
Conversely, Melzer's results of late have been poor, with the 33-year-old Austrian losing his sixth straight match as the left-hander limped into Flushing Meadows devoid of confidence.
Seeds Guillermo Garcia-Lopez and Jarkko Nieminen won their first outings of the tournament, moving into the last 16 with second-round victories.
Garcia-Lopez, the fifth seed from Spain, came from behind to down Germany's Dustin Brown 6-7 (5-7) 6-2 6-2.
Finland's Nieminen - seeded 15th - defeated another German Benjamin Becker 7-5 6-4 to progress.
All 16 seeds were given first-round byes.
In first-round results, Poland's Jerzy Janowicz had a 6-1 6-4 victory over Argentine Carlos Berlocq.
Janowicz, whose ranking has plummeted to 52nd after peaking at 19th earlier this season, hit seven aces and saved all five break points he faced to advance.
Sam Querrey was the only American through to the second round, as each of Wayne Odesnik, Robby Ginepri and Marcos Giron lost.
Querrey served 16 aces as he eased past Spain's Pere Riba 7-6 (7-5) 6-4.
Qualifiers Odesnik and Giron - both wildcard recipients for the US Open main draw - had their final competitive hit-outs before the New York major.
Odesnik fell 7-6 (7-4) 6-3 to Slovenia's Blaz Rola, while Giron - the world number 433 - was humbled 6-4 6-4 by Kazakh Aleksandr Nedovyesov.
France's Paul-Henri Mathieu dumped out wildcard Ginepri 6-3 7-5.
Canada's Frank Dancevic held off Brazilian Thomaz Bellucci 7-5 3-6 6-2 in two hours and five minutes, while France's Adrian Mannarino outclassed Bosnian qualifier Damir Dzumhur 6-2 6-2.
Federico Delbonis of Argentina progressed with a 7-6 (7-5) 6-4 win over Slovakian Martin Klizan, and Dutchman Igor Sijsling accounted for Kazakh Andrey Golubev 7-6 (7-5) 6-3.