The Sharks extended a 1-0 first period lead with a Jamal Mayers goal when Dave Bolland and Brent Seabrook went into the corner to the right of Marty Turco to get the puck. Neither came away with it, but John McCarthy did and found Mayers for his first goal of the year.
The Hawks responded quickly with a Jake Dowell tally after he took the puck from the end boards and stuffed one by Antii Niemi.
Boynton was benched for a good portion of the second period as it was his second miscue of the game that led to a Sharks goal.
The Hawks had a chance to cut the lead again but failed on a 44-second, five-on-three power play.