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.
"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.
Lazio went joint-second thanks to substitute Libor Kozak's header six minutes from time in a 1-0 home win over Sampdoria.
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.
"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.
