Milan left the field to the familiar sound of jeers from a sparse San Siro crowd of 27,000 after being outplayed by their promoted opponents, who should have taken all three points.
They have taken only five points in seven Serie A games since the Christmas break, a run which has included home defeats by Sassuolo and Atalanta, and have been knocked out of the Coppa Italia by Lazio.
Milan lost defender Alex to injury in the seventh minute, later confirmed as a broken nose, and Gabriel Paletta went off with a hamstring injury late on, leaving them to finish with nine men after using their three substitutions.
Empoli made the early running and Mario Rui nearly scored a stunning opener when he spotted Lopez off his line and just missed the target with a dipping effort from near the halfway line.
However, Milan went ahead with their first shot on target when Destro turned in Giacomo Bonaventura's low cross from close range, his first goal since his move from AS Roma.
Empoli deservedly equalised in the 69th minute when Massimo Maccarone escaped the attentions of two defenders and scored with a powerful downward header from Elseid Hysaj's cross.
Former Real Madrid keeper Lopez was dismissed with six minutes left as he handled outside the area, having got himself into the mess with a terrible clearance. Destro was substituted to make way for substitute goalkeeper Christian Abbiati.
"We conceded a soft goal and this is the disappointment from today," Filippo Inzaghi, Milan's third coach in just over one year, told reporters.
"We need to pick up a good win and we also have to get back some of our injured players. We lost Alex to a fractured nose and tomorrow he will be operated on.
"I haven't ever been able to field the same line-up for two matches in a row because I've always had players out injured or that aren't 100 percent."
(Writing by Brian Homewood in Berne; editing by Martyn Herman)
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