Hoglander had been acquired from the Vancouver Canucks for a third-round pick in the 2029 NHL Draft on June 29.
Steven Stamkos also scored and Juuse Saros made 29 saves for the Predators (1-1-0).
Miro Heiskanen scored for the Stars (1-1-0), and Casey DeSmith made 24 saves.
Dallas lost its season opener to the St. Louis Blues 4-0 at home on Friday.
Heiskanen gave the Stars a 1-0 lead just 47 seconds into the first period. After Saros made a save during a net-front scramble, Mikko Rantanen passed to Heiskanen in the right face-off circle for a blocker-side wrist shot.
Stamkos tied it 1-1 while on the power play at 4:46. Ryan O’Reilly threaded a backhand pass through two Dallas defenders for Stamkos, who one-timed a shot from the left circle.
The goal was the 625th in the NHL for the 19-year veteran, tying him with Jerome Iginla and Joe Sakic for 17th on the NHL's all-time list.
Hoglander put Nashville up 2-1 with another power-play goal at 15:49. Jack Ahcan’s shot from the left point deflected into the net off Hoglander’s left skate at the top of the crease.
Achan's assist was his first point with the Predators in his Nashville debut.
