Sinisa Mihajlovic's side were unable to take advantage of their better openings at San Siro after two goals early on in the fixture failed to decide the winner.
Milan and Lazio played out a 1-1 draw at San Siro that does little for the ever-declining continental qualification hopes of either side.
Marco Parolo, who scored twice against Milan last season, headed Lazio ahead from an early corner but the visitors' lead was short-lived.
Carlos Bacca hit back with a fine drive within six minutes to level the scores and Giacomo Bonaventura had a series of chances, but was unable to find the winning goal, while Senad Lulic was dismissed with six minutes to go for a second bookable offence.
Goalkeepers Federico Marchetti and Gianluigi Donnarumma were both in excellent form to ensure that the spoils were shared, which increases the pressure on beleaguered Milan coach Sinisa Mihajlovic, especially as club owner Silvio Berlusconi was in attendance.
The draw leaves Milan 11 points outside the Champions League places, while Lazio, who were eliminated from the Europa League in midweek, remain two spots and seven points below the Rossoneri in the table after playing out an eighth successive draw away from home in all competitions.
Donnarumma, called up to the Italy Under-21 squad for the first time this week, took his place in the Milan goal after recovering from a head injury sustained last weekend, while on-loan Alessandro Matri started for Lazio against his parent club.
The visitors built up early pressure and forced a string of corners after Antonio Candreva's strike deflected onto the roof of the net.
Lazio opened the scoring from that succession of set-pieces after eight minutes, Parolo rising highest and powerfully heading in Lucas Biglia's precise cross.
Bacca equalised six minutes later, the Colombia international breaking a run of four games without a goal or even a shot on target.
Luiz Adriano did superbly to hold the ball up inside the penalty area and Bacca latched onto his lay-off to thunder a terrific strike into the bottom corner with the outside of his right boot.
Bonaventura's header deflected wide after 27 minutes before Bacca's shot from a tight angle bobbled off-target and Bonaventura then smacked the crossbar with a 25-yard free-kick in the closing minutes of a frantic first half.
Seconds after the restart Bacca's shot was blocked by Marchetti and the goalkeeper tipped over a thumped drive from Bonaventura as Milan started the second half on top.
Donnarumma made a fingertip save to deny Felipe Anderson after 66 minutes as Lazio sought the decisive goal to earn their first win at Milan in Serie A since 1989.
Marchetti made a brilliant stop moments later from Bonaventura's close-range volley as the hosts pressed but, even after Lulic earned a second booking for hauling down Keisuke Honda, Mihajlovic's men could not make the breakthrough and the points were shared.
