Dallas (20-14-7) outshot the Red Wings 45-27, but went 0 for 7 on the power play.
The Stars had the first 12 shots on goal, but Zetterberg scored on the Red Wings' first shot 7:04 into the game.
Dallas tied it on Rich Peverley's short-handed goal with 7:13 left in the period.
Detroit's Justin Abdelkader missed a penalty shot with 5:58 left, but Andersson put the Red Wings back ahead for good lead with a shot from the right circle over starting goalie Dan Ellis with 1:55 to go in the first.
It's cool when you think about how many great American players have played the game and the two players that were at that 18-game point streak and what they've done in their careers. It's pretty cool right now, but it was kind of overshadowed by the loss.
— Blackhawks forward Patrick Kane after breaking the record for longest point streak by an American-born player with a goal and an assist in a 3-2 overtime loss against the Kings