It was Anderson's first shutout of the season, helping the Sting push their winning streak to five in a row.
Davis Brown and Alex Basso also scored for Sarnia (17-11-3).
Jake Paterson stopped 25 of 27 shots for Saginaw (12-15-4).
The Spirit controlled the play through out the first period and Anderson made at least four point-blank saves.
The Sting scored the only shot on a wrap-around goal from Brown.
The second and third periods were evenly played by both teams but Anderson continued to shine as Saginaw out shot Sarnia.
Galchenyuk's shot from the slot beat Paterson top shelf at 4:42 of the second.
Basso added an empty-net goal in the final minute of the game to wrap up the scoring.
Sarnia scored one power-play goal in seven chances and Saginaw went 0 for 5 with the man advantage.