It leaves the Mariners undefeated and pushes them just one point behind the league leading Brisbane Roar as the league remains tight at the top in the early stages of the season.
Adelaide got the first chance of the match away with Sergio Cirio hitting a curling strike that allowed the Mariners to counter and they found their goal on that counter.
The Mariners ran the ball up the field and Nick Fitzgerald was able to shoot and find the back of the net just 84 seconds in to the match.
From there the Mariners really dominated the match as they continually terrorised the Adelaide United defense but Fitzgerald, Marcos Flores and Mitchell Duke were not able to find the net for all those chances.
Adelaide started to come in to the match with Cirio looking dangerous but never really threatened the Mariners defense.
An error from Michael McGlinchey allowed Adelaide their best chance as he lost possession to Tarek Elrich who was only able to shoot wide.
McGlinchey had an opportunity to make up for that error moments later but he sent his free kick wide late in the half.
The Mariners had one last chance as Fitzgerald got on the end of Josh Rose's cross only for Galekovic to save and the cross par to deny the rebound, keeping it 1-0 at the break.
The second half saw much less action but still the Mariners were the dominant side with Matt Simon introduced part way through the second period for the Mariners.
In the 69th minute Galekovic was the only thing stopping Adelaide going further down as he palmed away McGlinchey's free-kick.
In the 80th minute the Mariners could have sealed it as Mile Sterjovski was able to get a chance away that bounced off the post for Simon who also hit the post with the rebound, allowing Adelaide to clear.
Adelaide United had some late chances to snatch a point but in truth never looked like finding an equalizer as the Mariners cruised to their victory.