The Metropolitan Police confirmed that two supporters in the visiting end were arrested in connection with two incidents in which pyrotechnics were set off.
A third fan was arrested for allegedly assaulting a steward, who had been investigating the setting off of the first pyrotechnic.
Police said five arrests were made in total, with two fans arrested before the game on suspicion of possession of Class A drugs.
The match at Stamford Bridge saw Palace secure their fourth straight Premier League win, which keeps the club four points clear of the relegation zone.
Cesc Fabregas had handed league leaders Chelsea an early lead in the derby clash with his fifth-minute tap-in, but Zaha's fine goal four minutes later restored parity for the Eagles.
The Ivorian then set up Christian Benteke for the winner just two minutes later, with Wayne Hennessey's string of superb saves and Mamadou Sakho's two last-ditch clearances late on ensuring Palace walked away from Stamford Bridge with a famous win.
Meanwhile, Chelsea's lead at the top of the table was cut to seven points following their fourth defeat of the season and Tottenham's 2-0 victory at Burnley.