Jimmy Howard, who became Detroit's starting goaltender last season in his fourth year with the team, made 21 saves for his fourth career shutout.
Modano, 40, grew up in the Detroit area and played his first 15 NHL seasons with the Minnesota-Detroit franchise. He eventually became the league's all-time leading scorer among American-born players and his goal Friday was his 558th.
Dallas released Modano following last season after the Stars missed the playoffs, but he said he felt he still had the skills to play and quickly signed a contract with Detroit.
Johan Franzen gave Detroit the lead 5:11 into the game and Modano scored just 24 seconds later. Pavel Datsyuk and Daniel Cleary added second-period tallies.
Jonas Hiller made 29 saves for Anaheim.
Detroit has won 14 of its last 15 home games against the Ducks.