Tatar opened the scoring off a backhanded pass from Brad Richards for a 1-0 lead with 8:30 left in the first period. Andrew Shaw then evened the score on a power play in the second period. Shaw sent a wrister past Jared Coreau, who was screened by Bryan Bickell, to make it a 1-1 game with 5:31 left in the second period.
Detroit (1-1) then scored three unanswered goals.
Justin Abdelkader scored on a power play breakaway against Michael Leighton to give the Red Wings a 2-1 lead less than two minutes later. Bickell had an opportunity to tie the game again on a breakaway of his own, but was denied by Coreau.
Tatar tallied his second goal off a rebound when Richards' shot bounced off Leighton at 4:24 in the third. He added an empty-netter with 1:34 remaining. Richards recorded an assist on each of Tatar's goals.
Vincent Hinostroza looked strong up front, recording three shots on net in more than 14 minutes of ice time. His presence was evident throughout the game, and he should be a stronger contributor in Rockford this season. Ryan Hartman also had three shots on net, while Viktor Tikhonov, who made his Blackhawks debut, had two shots in 15 minutes of ice time.
Trevor van Riemsdyk led the Hawks in ice time with 20:42. He also had two shots and a blocked shot.
Forward Daniel Paille and defenseman Jan Hejda, David Rundblad and Viktor Svedberg played in both games against Detroit. Paille and Hejda are both on professional tryouts.
Petr Mrazek started for the Red Wings in goal and stopped all 16 shots he faced. Coreau made 14 saves on 15 shots.
Corey Crawford stopped seven of the eight shots he faced. Leighton allowed two goals on 16 shots. Chicago (1-1) was 1-for-6 on the power play; Detroit was 1-for-4.
The Hawks travel to Montreal on Friday to play the Canadiens (0-1) at the Bell Centre.