A gritty right wing who entered the season with 144 penalty minutes and 10 goals, Bylsma scored the only goal Giguere needed 2:02 into the first period. He added his second career shorthanded tally early in the third to make it 3-0.
Bylsma, who had a trio of three-goal seasons with the Los Angeles Kings, already has four in nine games.
Giguere turned away seven shots in the first period, 12 in the second and five in the third en route to his fifth career shutout and first this season. He was hardly tested early as Atlanta went nearly 17 minutes before getting its initial shot.
In Saturday's 4-1 loss at Los Angeles, the Thrashers failed to get a shot in the first period. They have been outscored, 20-6, during a four-game losing streak.
Since winning just two of their first eight games, the Ducks have taken four of six.