Milan lacked guile in the first half with Robinho and Andrea Pirlo missing and Ronaldinho sold but as he so often does Zlatan Ibrahimovic opened the scoring with a brilliant opportunist strike from 20 metres early in the second half.
Lecce, who won at high-flying Lazio last weekend, hit the post before Ruben Olivera swept home following a corner on 82 minutes to grab a deserved point in their fight against the drop.
Milan also drew 4-4 with Udinese last Sunday as cracks begin to show in their title bid at the start of the second half of the season despite signing the mercurial Antonio Cassano.
"What Ibra did today was of extraordinary beauty and I'm sorry we've dropped two points from a game which we had in our grasp," coach Massimiliano Allegri told Sky.
"We conceded a goal in the only way we were going to."
Late winners from Lazio, Juventus and AS Roma kept the lucky trio on Milan's tail while resurgent champions Inter Milan, in sixth, beat Bologna 4-1 on Saturday and are now just nine points behind the leaders with two matches in hand.
The first game of the two is at home to Cesena on Wednesday.
Lazio went joint-second thanks to substitute Libor Kozak's header six minutes from time in a 1-0 home win over Sampdoria.
The Czech striker, expected to leave the Rome club in the January transfer window, looked just ahead of the last defender as a free-kick was swung into the box but he celebrated wildly nonetheless and ripped his shirt in the process.
Lazio, surprise packages having been relegation candidates last season, moved level with Napoli after Walter Mazzarri's side could only draw 0-0 with Fiorentina on Saturday.
Fourth-placed Roma's 89th-minute goal in the 1-0 win at Cesena could have been chalked off too with Adriano appearing to be just in front of the defenders during a scramble.
JUVENTUS WIN
His shot, after Marco Borriello hit the bar, was saved and Simplicio also looked a touch offside as he put the ball back across the goal and it went in off Maximiliano Pellegrino.
"The referees have said they'll never spot that centimetre. it's not worth discussing," Roma boss Claudio Ranieri said.
Alberto Aquilani's volley 11 minutes from the end deflected in off team-mate Giorgio Chiellini to wrongfoot the goalkeeper and give fifth-placed Juventus a 2-1 win over bottom side Bari.
Juve have yet another injury crisis and Alessandro Del Piero, 36, was the only one of five first-team strikers fit.
The hosts laboured until Del Piero curled in a trademark free-kick just before the break but Bari equalised early in the second half when new signing Gergely Rudolf easily beat Gianluigi Buffon, playing his first league game since May.
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