The Galaxy (7-2-7) secured their second win in the last seven matches to remain unbeaten at home this season.
Dallas (3-7-4) was looking for its first road win of the season, having only managed two draws and five losses.
Joveljic opened the scoring in the fourth minute on a wide-open shot from the penalty spot, and he added his ninth goal of the season on a penalty kick in the 66th for a 2-1 lead.
There was a wild sequence in the 32nd minute. Maarten Paes dove to his right to deny Gabriel Pec’s penalty kick and the Dallas goalkeeper also blocked the rebound attempt before Joveljic sent it into the back of the net. But the play was called back for offside.
Puig, who scored the game-winner on Saturday against Houston, added a goal in second-half stoppage time after an individual effort. He dribbled it from midfield, getting past a defender, and cut back another defender in the box for a shot on the outside of his right foot.
The Galaxy hold a 27-9-6 record in 42 all-time regular-season matches played at home against Dallas.
Patrickson Delgado scored for Dallas in the 22nd with a redirection that glanced off the crossbar. Dallas defender Nkosi Tafari was sent off in the 82nd after his second yellow card.