Goffin endured an injury-plagued season in 2021 during which he only managed to play in 29 games. The 31-year-old is slowly beginning to make his return to competitive tennis and the straight sets win over Bagnis is a major milestone for the Belgian.
The previous season came to an end for Goffin during September's US Open. The player endured knee problems and unsurprisingly lost 3-0 to Mackenzie McDonald.
His first game since that loss came last Thursday at the Melbourne Summer Set where he lost 2-0 to Slovakia's Alex Molcan.
Nevertheless, Goffin was able to shake off the cobwebs relatively quickly and win his following game against Bagnis 6-4 6-4.
The player is now through to the second round and will take on either Argentina's Federico Delbonis or Spain's Albert Ramos-Vinolas next.
Elsewhere, fifth seed Lorenzo Sonego bounced back from losing the first set to France's Hugo Gaston, with the Italian moving into the last-16 courtesy of a battling 3-6 6-3 7-5 victory.
Compatriot Fabio Fognini, seeded seventh, was given relatively few problems in a 6-3 7-5 win over Germany's Daniel Altmaier while Australian wild card Jordan Thompson thrashed America's Marcos Giron 6-4 6-2.
In the Adelaide International 2, seeded pair Alexander Bublik and Frances Tiafoe tumbled out after straight sets defeats.
Kazakhstan's Bublik, seeded sixth, was beaten 7-6 (5) 6-2 by Australian wild card Aleksandar Vukic while Tiafoe, seeded seventh, was brushed aside 6-2 6-3 by fellow American Tommy Paul.
Spain's Jaume Munar hammered home hope John Millman 6-2 6-2 while France's Arthur Rinderknech prevailed 6-3 6-7 (5) 6-3 in a tense tussle against Mackenzie McDonald of the United States.