Simone Inzaghi's team are already 4-1 down to the defending European champions after the first leg of their last 16 tie.
Despite Friday's win, Lazio are still only seventh in Serie A, while Crotone are anchored to the foot of the table seven points adrift of safety.
Lazio took the game to the Stadio Olimpico visitors but were pegged back the first two times they went ahead.
A cool finish from the six-yard line from Sergei Milinkovic-Savic on 14 minutes gave Lazio the lead before Nigerian forward Simeon Tochukwu Nwankano levelled.
Luis Alberto restored Lazio's lead on 39 minutes only for Nwankano to equalise again with a 50th-minute penalty.
However, substitute Felipe Caicedo secured the three points for Lazio six minutes from time.
Atalanta climbed into the top four when they powered past Spezia 3-1 in Friday's late game largely thanks to a Mario Pasalic double.
His two second-half strikes came either side of a 55th minute goal from in-form Muriel.
Roberto Piccoli pulled a goal back in the 81st minute for Spezia, who are six points clear of the drop zone in 16th.
Atalanta have their own Champions League worries after losing their home first leg of their last 16 tie 1-0 to Real Madrid.
The weekend's big games see AC Milan host Napoli Sunday, while Inter Milan visit Torino and Caglairi host Juventus the same day.