Milan, third in the league standings on 56 points, broke the deadlock in the 88th minute when substitute Okafor scored on a rebound from near the penalty spot.
Lazio were down to 10 men in the 57th minute when defender Luca Pellegrini received a second booking for trying to unlawfully stop Christian Pulisic after losing the ball. The hosts ended the match with eight players after defender Adam Marusic and midfielder Matteo Guendouzi were also sent off.
Milan are one point adrift of second-placed Juventus who travel to Napoli on Sunday and 13 behind leaders Inter Milan, who host Genoa on Monday.