The 39-year-old, who had not featured since sustaining a knee injury against Juventus in May, tapped in Milan's second after 67 minutes, seven minutes after he came off the bench.
"Ibrahimovic never gets old and he has great passion, a fire burning inside him," Milan coach Stefano Pioli told DAZN.
"He competes to win, he always trains to the maximum and he does so with pleasure. When you are like that you do not feel the years go by."
The result put the Rossoneri top of the table with nine points, ahead of Napoli on goal difference, while Lazio are sixth with six points after three games.
"We are still dreaming big, but we must dream at night and work during the day to make them come true," Pioli said.
It could have got even better for the hosts when Ciro Immobile kicked Kessie's foot and conceded a penalty, but the Ivorian midfielder struck the bar from the spot deep in first half stoppage time.
The home fans roared with approval when Ibrahimovic stepped onto the pitch for the first time since May and he quickly made his mark when Rebic's cross put the ball on a plate for him to score.
Tensions boiled over at the full-time whistle as opposing players and staff came together on the touchline, leading to a red card for Lazio coach Maurizio Sarri.