Chiesa, fresh off his first appearances for Italy, drew a penalty that Jordan Veretout converted near the half-hour mark.
Then Simeone came off the bench and scored between two defenders midway through the second half.
”These kids are strong and have a lot of character and personality,” Pioli said.
The only negative note for Fiorentina was a yellow card picked up by Chiesa that will rule him out of Saturday’s match at third-place Roma.
Both Chiesa and Simeone are the sons of prominent players.
Chiesa’s father, Enrico, also played for Fiorentina and Italy while Simeone’s dad, Diego, was a standout for Argentina and now manages Atletico Madrid.
In the 13th minute, fans applauded in Astori’s honor since the defender wore the No. 13 shirt.
Udinese has lost seven straight, setting a club record.
The Milan derby is one of four more postponed matches that will be made up on Wednesday.
EUROPA LEAGUE PLACES
In a match featuring two clubs within striking distance of the Europa League places, Sampdoria won 2-1 at Atalanta by taking advantage of two defensive errors.
Gianluca Caprari scored after defender Rafael Toloi slipped on the rain-slickened pitch. Then after Toloi’s equalizer, Duvan Zapata ran onto an errant back pass by Nicolas Haas and scored his 10th of the season.
Atalanta, Fiorentina and Sampdoria are level on points.
Genoa beat relegation-threatened Cagliari 2-1 with a last-minute goal from Iuri Medeiros.
Medeiros, a 23-year-old on loan from Sporting Lisbon, scored with an expert control and curving shot.
Gianluca Lapadula had put Genoa ahead with a header early in the second half and Nicola Barella equalized with a penalty.
It was the sixth goal this season for the 21-year-old Barella, making him the youngest midfielder to score more than five goals in Europe’s five major leagues this season.
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