Milan got off to the ideal start when Lucas Biglia's volley was deflected into the net off Empoli's Leonardo Capezzi in the 10th minute.
Terracciano denied them a second goal before halftime with a double save from Giacomo Bonaventura and he also blocked Franck Kessie's effort from the rebound.
Milan then gifted Empoli an equaliser in the 71st minute when Biglia gave away a penalty after Milan captain Alessio Romagnoli had sent an attempted clearance straight to an opponent. Francesco Caputo converted the spot kick.
Terracciano then capped his outstanding evening with a superb save to turn Suso's shot around the post, leaving Milan with six points from five games and a modest 13th in the table.
Earlier, upstarts Sassuolo leapt into third place with a 2-0 win away to SPAL.
Claud Adjapong scored from a rebound just before the hour and Alessandro Matri added the second with a shot which went in off the post. Sassuolo have 13 points from six games, two behind second-placed Napoli.
"We have got what we deserved from these six games and we are enjoying the moment," said Sassuolo coach Roberto De Zerbi.
(Writing by Brian Homewood; Editing by Toby Davis)
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