Giampaolo Pazzini was on target twice for the Rossoneri, who played over 70 minutes with an extra man following a red card to Antonio Candreva.
Kevin-Prince Boateng also found the back of the net as Milan moved a point above their opponents and into a qualifying berth for the Champions League next season.
Milan soon made it clear they meant business when Stephan El Shaarawy tested Federico Marchetti at his near post in the fourth minute.
Moments later, El Shaarawy appeared to be fouled inside the penalty area, but the referee waved play on as the ball fell to Pazzini, but his shot was deflected off the goal line by a Lazio defender.
At the other end, Candreva teed up Sergio Floccari, who gave Abbiati a rare touch of the ball with a weak shot from 15 yards, but Milan were soon back on the attack again.
The only way Candreva could find to denying El Shaarawy a goalscoring opportunity was to tug his shoulder, earning a red card after the Milan striker tumbled to the deck, although the referee ignored Milan's pleas for a penalty and instead awarded a free-kick on the edge of the penalty area.
It took Milan surprisingly long to make their extra man count, but they finally made the breakthrough five minutes before half time,
Pazzini, deputising for the injured Mario Balotelli, was on hand to score after the ball was touched away from El Shaarawy inside the six-yard box.
Pazzini was certainly making his presence felt, all the while giving coach Massimiliano Allegri a selection headache, and his header brought a fine one-handed save out of Marchetti, who was helpless to prevent Boateng from slotting in the loose ball to make it two just before half time.
The chances of Lazio recovering were ultimately ended on the hour mark when Stefan Radu made a hash of his clearance, presenting the ball to Pazzini who lashed it in low from 20 yards.
M'Baye Niang struck the top of the crossbar late on, but no further damage was inflicted as three goals were enough for three points.