Yıldız was brought on in the 61st minute on Sunday with Juve trailing 4-2 and Inter seemingly headed for an important victory before the 19-year-old's late double.
"I want to thank the team, the coach and my family: it was not easy, but I am very happy," Yildiz said. "You always have to stay together and play as a team; in soccer everything can change quickly."
Inter remained second — four points behind Serie A leaders Napoli, and one point ahead of Juventus.
Juve's No.22 Tim Weah scores in the eight-goal thriller in Milan. (AP PHOTO)
Nicknamed "Italy's derby," matches between Inter and Juventus are always huge fixtures in the Serie A calendar and the two teams are considered the main title contenders, along with Napoli.
Inter took the lead in the 15th minute when Piotr Zielinski struck a penalty straight down the middle after Marcus Thuram had been fouled by Danilo.
The Nerazzurri had conceded just two goals in their past four matches but they let in as many in six minutes as their defence was caught napping.
First, Juan Cabal floated a delightful ball over the top for Weston McKennie to cushion across to Dusan Vlahovic, who tapped it in from point-blank range.
Shortly afterwards, Francisco Conceicao dribbled down the right and got past Henrikh Mkhitaryan all too easily before rolling across for Tim Weah to slot home.
Mkhitaryan atoned for his error with a wonderful equaliser in the 35th minute, playing a one-two with Thuram and feinting past a Juventus defender before firing into the bottom left corner.
Inter turned the match around completely two minutes later with another penalty after Pierre Kalulu clattered into the back of Denzel Dumfries.
Juventus goalkeeper Michele Di Gregorio got a hand to Zielinski's kick but couldn't prevent it going into the bottom left corner.
Inter extended their lead eight minutes into the second half. Danilo tried to head a corner clear but it came to Dumfries who drilled it into the far bottom corner.
Juventus got back into the match in the 71st. McKennie picked out Yıldız, who was unmarked in lots of space on the left, and he surged downfield before firing across into the bottom right corner.
Inter were to regret their missed chances as Yıldız doubled his tally eight minutes from time when he powerfully fired home Conceicao's cross.
Genoa director Marco Ottolini said Mario Balotelli will sign on Monday "barring surprises" and the team desperately needs the former Inter and Manchester City forward.
Genoa had just two shots on target in a 3-0 loss at Lazio as they fell to their fifth defeat in six matches.
Parma came back to draw 1-1 against Empoli and could have won the match late on but Ange-Yoan Bonny's penalty struck the crossbar, two minutes after Gabriel Charpentier had levelled.
Monza twice fought back to salvage a 2-2 draw with Venezia.
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