Gasperini was livid after Fiorentina, who climbed to third in the table, took the lead from the softest of penalties for an alleged foul on Federico Chiesa in the 63rd minute.
Chiesa burst into the Atalanta area, slowed down and dribbled across the path of defender Rafael Toloi who did everything possible to avoid any contact, yet the Fiorentina player still went flying.
Surprisingly, the referee awarded a penalty without consulting the VAR system and Jordan Veretout converted. Cristiano Biraghi scored the second in the last minute.
As the final whistle went, Gasperini began ranting angrily and wagging his finger at Pioli and there appeared to be a push between the pair before they were separated.
"What happened today is inconceivable in the modern era," Gasperini said. "It was a penalty from the past......it is difficult to accept this situation with technology. It is a clear and obvious episode."
Pioli stood by 20-year-old Chiesa, who is regarded as one of Italy's most promising players.
"Chiesa is a player who has improved enormously. Obviously, he may fall over if there is a physical contact but he doesn't go to ground at the slightest touch," he said.
Fiorentina have 13 points, ahead of Inter Milan and Sassuolo on goal difference.
AC Milan made surprisingly light work of surprise packages Sassuolo -- who would have gone second with a win -- as they won 4-1 away to end a run of three successive draws.
Franck Kessie collected the ball in his own half, powered forward and scored from the edge of the area to give Milan the lead before halftime.
Suso and Samu Castillejo scored with long-range left-foot shots after the break and, although Filip Djuricic pulled one back for Sassuolo, Suso fired in a fourth in stoppage-time.
Genoa striker Krzysztof Piatek continued his remarkable start to his Serie A career by notching a brace in a 2-1 win at lowly Frosinone, who at least had the consolation of scoring their first goal of the season.
Piatek volleyed home in the 33rd minute and the Pole turned in a Christian Kouame cross from close range three minutes later, his eighth goal in six appearances since joining from Cracovia for a modest four million euros ($4.64 million) in July.
Promoted Frosinone, who have one point, finally scored when Camillo Ciano converted a penalty three minutes before halftime after Nicolas Spolli fouled Stipe Perica.
Former AS Roma and Arsenal forward Gervinho grabbed the only goal to give Parma a 1-0 win over Empoli in a game between the other two promoted sides.
It was a third win of the season for Parma who were relegated to the fourth tier in 2015 after going bankrupt and have bounced back to the top flight with three successive promotions.
Torino won 1-0 at Chievo after forward Simone Zaza came off the bench to grab a late winner, leaving the Flying Donkeys rooted to the bottom of the table with minus one point after having three deducted for accounting irregularities.
($1 = 0.8615 euros)
(Reporting by Brian Homewood,; Editing by Toby Davis and Ed Osmond)
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