Going into the game, the Bite knew they needed a series win to stay a realistic chance of making the playoffs but things got off on the wrong foot.
Aces slugger Justin Huber belted a two-out, two-run homer off Zac Fuesser in the bottom of the first, giving the home team a lead it would never surrender.
The teams exchanged some scoreless innings before Bite designated hitter Adam Kam cut the margin in half in the fifth, Ethan Paquette and Chris Adamson helping to bring him home.
Carlo Testa answered back for the Aces at the bottom of the sixth, striking a solo shot over the centre field wall to make it 3-1 in a low-scoring contest.
Adelaide got runners on in the seventh and eighth frames, but couldn't convert, leaving a two-run deficit coming into the last.
Quincy Latimore fought off big league pitcher Travis Blackley before putting a home-run over left field to make it a one-run game, but that was as close as it got, the Oakland Athletics reliever recovering to earn the save.
The Bite's lead-off hitter Jeremy Cresswell was the shining light for the offence, picking up half of the team's eight hits.
John Hussey got the win for Melbourne, while Adelaide couldn't find a fitting send off for Fuesser, who has been shut down by the Pittsburgh Pirates and returns to the USA on Tuesday.
The Bite need to win the remaining three games of the series to keep itself in the post-season hunt.
Seon Gi Kim takes the mound for Adelaide in game two, scheduled to face off against Kevin Reese.