Joaquín Correa scored the second for seventh-place Lazio. Crotone remained bottom with just two points from its opening eight matches.
Lazio’s match was at risk of being postponed after torrential downpours and flash flooding in the area. But it went ahead despite the ball barely rolling and water splashing up from the waterlogged pitch as the players ran.
It was Immobile’s first match in nearly three weeks after being ruled out with COVID-19, which also kept him out of Italy’s three matches.
Immobile had scored in his previous three matches before his layoff and he opened the scoring in the 21st minute with a diving header into the bottom left corner following a superb cross from Marco Parolo.
Correa doubled Lazio’s lead in the 58th with a shot from a tight angle after dribbling past Crotone defender Pedro Pereira and going almost to the byline.
Atalanta and Spezia both struggled in a match of few chances.
Spezia had won only one of its last five matches but almost took a surprise lead within the first two minutes when Diego Farias’ curled effort smacked off the far post.