Adam Marusic got the visitors off to a perfect start with a fine solo goal inside three minutes, before Joaquin Correa latched on to Ciro Immobile's header and fired home in the 51st minute to put Lazio on course for a comfortable win.
Looking to make amends for their midweek Coppa Italia defeat by Atalanta in Bergamo, Lazio had chances to make it three before Mario Pasalic got the hosts back in the match with 11 minutes to go.
However, substitute Vedat Muriqi made sure of the win three minutes later as Lazio moved level on 37 points with fourth-placed Roma, who host Verona later on Sunday. Lazio were briefly fifth before Napoli beat Parma 2-0 to go fourth.
"We have great mental strength," Lazio assistant Massimiliano Farris told DAZN. "In the Coppa Italia [on Wednesday] we went out undeservedly. Today, we played a strong game and we won in a more than deserved way.
"Lazio-Atalanta has become a classic. Today it was important to overtake them in the standings."
The previous four meetings in all competitions between the sides had produced 21 goals, and it took only just 126 seconds for the net to bulge on Sunday as Marusic struck from 20 metres for his second league goal of the season.
Lazio's second was very much route one with their top scorer Immobile turning provider, but he and his teammates should have put the game to bed from a hatful of chances in the second half.
Pasalic's goal only unnerved the visitors momentarily, however, as Kosovan striker Muriqi's first Serie A goal wrapped up the points in the 82nd minute.