Ayala was sent-off in the 61st minute of Wednesday night's clash for a challenge on PNE winger Brandon Barker just outside the box.
From the resulting free-kick, Paul Gallagher scored PNE's equaliser and Jayden Stockley went on to head the winner nine minutes from time.
Referee Keith Stroud showed centre-half Ayala a straight red card for the challenge.
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A statement from the FA released on Friday afternoon read: "Following an Independent Regulatory Commission hearing today, Daniel Ayala will be available for Middlesbrough’s next three matches.
"The defender was sent off for serious foul play during the game against Preston North End on Wednesday [13/03/2019] but a claim of wrongful dismissal was subsequently upheld."
Speaking immediately after the game at the Riverside Stadium, PNE manager Alex Neil said:"I think the issue you’ve always got with a sending off like that one is what are the rules nowadays?
"If the rule is if you win the ball then it’s not a sending off then the lad certainly won the ball.
"If the rule looks at how quickly you go into the ball and how high the foot is and a whole host of other things then you could understand why it might be a sending off."
Boro manager Tony Pulis described the red card for Ayala as a 'poor, poor decision'.