It was Stefano Bioli's first match as coach of Milan, succeeding Marco Giampaolo who was sacked earlier this month.
Hakan Shalhanoglu scored Milan's opener in the first half but Lecce equalized in the second half through Khuma Babiker.
Substitute Kashishtov Puntec restored Milan's lead with nine minutes remaining, but Calderoni's long-range shot in the 92nd minute gave the visitors a draw.
AC Milan now have 10 points, 12 points temporarily, while Lecce stopped the defeats in the last two rounds, snatching a precious point that left it with 7 points in 15th place.
The Rossoneri continue their run of negative results at home for the third consecutive game, with two losses (against Inter Milan and Fiorentina), and then drawn today.