Domenico Berardi had given the home side the lead from the penalty spot in the 26th minute, before Italy international Ciro Immobile pulled Lazio level two minutes before halftime, ghosting into the box to score his 18th league goal of the campaign.
Lazio came out far stronger after the interval and coach Simone Inzaghi used all three substitutes in a bid to get the winner.
His final change paid off as Cristiano Lombardi sent in a low cross which Acerbi inadvertently sent trickling over the line.
The home side had two chances to snatch a late equaliser, however, with winger Lorenzo Pellegrini striking the bar with a header and Berardi firing wide in stoppage time from inside the area.
Lazio are fourth on 60 points, three behind third-placed Napoli, who play leaders and champions Juventus on Sunday.
Second-placed Roma can provisionally cut the gap between them and Juve to five points if they beat Empoli at home later on Saturday.
(Reporting by Richard Martin; Editing by Toby Davis)