Tsitsipas, who strung together four consecutive wins over top-10 players in Toronto before falling to world number one Rafael Nadal in Sunday’s final, converted just one of eight break points as he was sent packing.
For Goffin, who won 73% of his first serve points, the win avenged a quarter-final loss to world number 15 Tsitsipas in Washington two weeks ago.
Goffin will next face Frenchman Benoit Paire.
In other action, Korean Chung Hyeon rallied to beat Jack Sock 2-6 6-1 6-2 and set up a second-round clash with Argentine fourth seed Juan Martin del Potro.
Chung, an Australian Open semi-finalist who in April went on to become the first Korean to crack the top 20 of the ATP world rankings, won 70% of his first-serve points en route to the win.
The clash with Del Potro, who this week rose to a career-high third in the world rankings, will be the first meeting between the two players.
For Sock, who has not won since the first round in the Italian Open, the defeat marked his eighth consecutive loss.
Dutchman Robin Haas beat Serbian Filip Krajinovic 4-6 6-2 6-3 to set up a second-round clash with German third seed Alexander Zverev while Canadian Milos Raonic beat Serbian Dusan Lajovic 6-3 6-3 and will next face Tunisian lucky loser Malek Jaziri.
Swiss second seed Roger Federer, the top player in the men’s draw following Nadal’s withdrawal on Sunday due to fatigue, will kick off the evening session with a second round clash against German Peter Gojowczyk.
