Sassuolo went on a counter from a Fiorentina corner, goalkeeper Alban Lafont palmed the cross to the edge of the box, where Duncan controlled to fire home.
Alfred Duncan scores season's first league goal for Sassuolo
The Ghana international opened the scoring in the 62nd minute after smashing in a a left-foot scorcher.
Duncan turned provider when he burst down the left and rolled across for Khouma Babacar, who was left criminally unmarked to tap in from eight yards to make it 2-0 in the 67th minute.
READ ALSO: undefined
Two minutes later, Edimilson Fernandes' daisy-cutter from outside the penalty area bounced off the upright and into the path of Simeone to tap in.
Stefano Sensi restored Sassuolo's two-goal lead with a thunderbolt which swerved goalkeeper Lafont.
But the visited did not give up and Marco Benassi reduced the deficit with a tap-in from close range after an Edimilson Fernandes glancing header was parried from point-blank range.
In stoppage time, Kevin Mirallas snatched a dramatic equalizer with an angled drive which squirms under the arms of goalkeeper Consigli for his first Serie A goal.