Kaka scored an excellent opener for the Rossoneri, but the hosts were unable to hold on and they dropped points again by conceding in the second half
The Brazilian combined with Mario Balotelli nine minutes after the interval, sending a sumptuous curling effort into the top right corner in a true moment of quality in an otherwise dour affair.
It was Kaka's first goal of the season, but it was not enough for Milan to seal three points as Mickael Ciani headed home from an Antonio Candreva cross with 18 minutes to go to secure his side a point.
Kaka was given just his second league start of the season as Massimiliano Allegri made four changes from Sunday's 3-2 defeat at Parma, while Lazio boss Vladimir Petkovic also rotated heavily.
Balotelli, who came in for criticism from Allegri after his performance on Sunday, tested Lazio goalkeeper Federico Marchetti as early as the second minute, driving into space before unleashing a shot from 25 yards which the goalkeeper parried low to his right.
Kaka was next to threaten for the hosts, fizzing an effort narrowly over the bar from 20 yards in the 14th minute following a swift counterattack.
The Brazilian went even closer four minutes later, dragging his shot just wide of the left post after being found inside the box by Sulley Muntari.
Miroslav Klose wasted Lazio's first real chance of the game five minutes after the break, with the veteran's touch letting him down when better control would have seen him with just Milan goalkeeper Gabriel to beat from eight yards.
Four minutes later Kaka put Milan in front, receiving Balotelli's pass from the left before curling an unstoppable shot beyond a helpless Marchetti from 20 yards.
It was not enough to stop the visitors though, who despite showing little attacking threat, equalized with 18 minutes to go. French defender Caini was the scorer, rising unchallenged to glance home Candreva's cross from the right from six yards.