Roberto De Zerbi's exciting team is on seven points after three games and cannot be caught until Monday (AEST).
Sassuolo is a point ahead of five teams, including Napoli, which takes on champion Juve on Monday (AEST), Inter Milan and Atalanta, who are all expected to challenge for the Serie A title this season.
Caputo, known as "Ciccio" in Italy, was called up for Italy on Saturday (AEST) ahead of matches against Moldova, Poland and Netherlands during the next international break, and the 33-year-old celebrated with a clinical performance that took him to three goals in as many games this season.
He struck from the penalty spot in the 58th minute to put the hosts in the lead, just nine minutes after Simy had levelled Domenico Berardi's first-half opener with a penalty of his own for Crotone.
The forward made it 3-1 with five minutes remaining after being put clean through by Berardi before Manuel Locatelli completed the rout with a close range finish deep into stoppage-time.
Roma finally notched up its first win of the season, Spanish forward Pedro Rodriguez, who signed a three-year deal with the capital club last in August after leaving Chelsea on a free transfer, scoring in the 55th minute to seal a 1-0 win over Udinese.
Pedro seized on a weak clearing kick and hit the ball from long-range, going in off the post for his first goal for his new club.
The other match scheduled for Sunday (AEST) – Genoa's home clash with Torino – was postponed earlier in the week followed a raft of COVID-19 cases for the host, which rose to 22 among playing and coaching staff.
Both Napoli and Atalanta announced new cases among playing staff on Sunday (AEST), with Gennaro Gattuso's side now counting midfielder Eljif Elmas among those with the virus after Poland international Piotr Zielinski was revealed as testing positive on Saturday (AEST).
However Juve coach Andrea Pirlo said that he did not believe there was "any risk" of the match not being played.
"I don't think there will be problems that mean we can't play the match," he said.
"We've prepared for the match like all the other teams have so tomorrow evening we will be ready to play. It (the situation) hasn't changed anything for us at all."
But a later round of testing showed two positive cases among Juve staff, though not connected with the playing squad, management or medical teams.
The squad, as a consequence, will conduct isolated training ahead of the match.
No Napoli players have been called up to the Italy squad, with the Italian Football Federation saying that the decision to not select the club's players was a "precautionary" measure after the surge in cases.
Atalanta said one case "with low viral load was diagnosed within the team group", adding that the unnamed player was asymptomatic.