Vernon Fiddler and Sheldon Souray scored for the Stars, who were outplayed for most of the game by the energized Blackhawks before a crowd of 21,674.
Chicago ended a four-game losing streak against Dallas by taking the second contest of a home-and-home set. The Stars had won 2-1 Friday night in Dallas in both clubs' season openers.
Chicago's Corey Crawford made 19 saves.
Dallas' Andrew Raycroft stopped 26 shots, following a 37-save effort by Kari Lehtonen on Friday.
Chicago outshot Dallas 10-2 in the first period and took a 1-0 lead 8:06 in on Brunette's first goal as a Blackhawk. The 38-year-old forward, who signed as a free agent in the offseason, poked in a rebound of Sharp's shot from the left circle during a power play.
Chicago kept up the pressure in the second, and built a 3-0 lead on goals by Bolland and Toews.
Bolland fooled Raycroft with a 50-foot shot from the left wing boards to make it 2-0 at 7:39. Toews scored just under four minutes later on a breakaway after he left the penalty box, skated to the Dallas blue line and took a stretch pass from Brent Seabrook.
Fiddler's rising shot from a sharp angle beat Crawford with 7:25 left in the second to cut it to 3-1.
Sharp made it 4-1 at 5:10 of the third when he fired a shot over Raycroft's glove on a 2-on-1 break during a delayed penalty call.
Souray's screened power-play goal midway through the third trimmed it to 4-2. Bolland dumped in an empty-net goal with 1:46 left to complete the scoring.
Notes: Bolland had a strong performance after missing Friday's game with an upper-body injury. ... Souray's goal was his first in the NHL since Jan. 20, 2010. He played last season with Hershey of the AHL. ... Chicago skated without LW Viktor Stalberg (lower-body) and RW Ben Smith (concussion) for the second straight game. ... D Nicklas Grossman (hip) and D Adam Pardy (ribs) were out for Dallas for a second night. ... The Blackhawks recalled C Markus Kruger from Rockford of the AHL in time for the game and assigned C Brandon Pirri to their top farm team.