Arsenal led the league for 248 days this season but did not end up winning it.
Jorginho, who helped Italy win the European Championship in 2021, spent four and a half years at Chelsea after joining from Napoli.
The draw came at a cost for Manchester United with their French defender Raphael Varane leaving the pitch in tears, raising concerns over his participation in the World Cup.
Arsenal had to come from behind twice before the lucky bounce from Jorginho's shot made it 3-2 in the third minute of stoppage time.
Seven players have arrived at Stamford Bridge this month, including Ukraine winger Mykhailo Mudryk in a deal worth around $108 million and France center back Benoît Badiashile for $40 million.
Jorginho converted the spot-kick and Pierre-Emerick Aubameyang doubled Chelsea’s advantage in the 34th minute to help the Blues to their first win on Italian soil since 2003.
Second-place Manchester City can trim the gap to Arsenal to two points with a win at Tottenham on Sunday, though Arsenal would still have a game in hand.
Italy lost to North Macedonia in the WC qualifying playoffs on Thursday and failed to qualify for the mega showpiece for the second straight time.