In the battle of the birds, The Magpies kept the Swans goalless for the opening half and piled on 12 of their own to lead by 73 points at the major break.
The second quarter was when Euroa truly broke the game open, kicking eight goals in that term alone.
The lead extended to 77 at three-quarter time as the Swans kicked their first two goals of the match before Euroa finished the stronger to complete a 90-point win, running out winners 19.10 (124) to 4.10 (34).
Tristan Davies and Jett Trotter kicked four each, Ben Bath booted three and Matthew Ivill and Peter Cairns added two apiece as the other multiple goalkickers for the Magpies.
Davies efforts take his season tally to 20, while Trotter has now kicked 14 for the season across five matches.
Jayden Gleeson was named best on for the home side, while other players to perform in the win were Max and Jacob Gleeson and Ben Harrison.
Swan Zac Alderton kicked all of his team's goals, while Bryden Squire was named the best Swans player on the ground.
Ethan Warburton, Max Clohesy, Diesel Batey and Luke Moore were other players who gave their all in the loss.
The Magpies now have five wins for the season and will travel to Mooroopna to take on the Cats in round seven.
On the other hand, the Swans, who sit in 10th position, will have its hands full when they host Echuca, which is on a five-game winning streak.
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