Bosnia forward Dzeko's brace took his tally for the season to 33 goals in all competitions - eclipsing the previous record jointly held by club captain Francesco Totti and two other Roma legends.
His two goals, typical close-range poachers' efforts either side of the interval, clinched a comfortable win against an Empoli side with the poorest strike rate of any club in the Italian top flight.
The three points lifted Roma to within five points of leaders Juventus, 24 hours before the champions travel to third-placed Napoli for star striker Gonzalo Higuain's first return to his former club.
A victory in that highly-charged encounter will leave Juve looking like very short-odds favourites to go on and clinch their sixth consecutive Scudetto.
Dzeko's goals saw him pass Totti's best return, in the 200-07 season, as well as the totals registered by Rodolfo Volk in 1930-31 and Argentine striker Pietro Manfredi in 1960-61.
The former Manchester City player has scored 23 league goals, eight in the Europa League and two in the Italian Cup.
Lazio had earlier boosted their hopes of Champions League football next season by coming from behind to snatch a 2-1 win at struggling Sassuolo that leaves them fourth, three points adrift of Napoli in the final qualifying spot for Europe's elite competition.
A late own goal by Sassuolo defender Francesco Acerbi gave Simone Inzaghi's side all three points after Ciro Immobile's 18th league goal of the season cancelled out Domenico Berardi's penalty opener for the home side.
The win was a tactical coup for Inzaghi with all three of his substitutes having a role in the move that led to the 83rd-minute winner in the first of three matches in eight days that could define the club's season.
On Tuesday, Inzaghi's men will defend a 2-0 first-leg advantage in their Italian Cup semi-final clash with local rivals Roma before hosting Napoli at the Stadio Olimpico on Sunday.
"It is a very important win against a very well organised side," Inzaghi said. "It is not easy for anyone to win here."
The Lazio boss denied that he would be cheering on Juventus on Sunday.
"I don't pay much attention to the others," he said. "On Tuesday we have the match with Roma, which will be very important, and on Wednesday I will start thinking about Napoli next weekend. Now I am only thinking about Roma."