The 30-year-old, who previously played on loan at West Ham, now stars for Portuguese champions Benfica.
Benfica had lost all four of their previous matches in the competition and sit bottom of Group D but got off to a flying start.
After just five minutes, ex-Inter man Joao Mario opened the scoring with a half-volley finish from inside the area.
He then netted a second from close-range just minutes later before sealing his hat-trick just after the half-hour mark.
At full-time, teammate Casper Tengstedt handed Joao Mario the match ball for his hat-trick but he just threw it away on the turf in frustration.
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Whilst scoring three goals in a match is a huge personal achievement, keeping that ball would not have been a welcome souvenir as Benfica threw the match away.
Joao Mario's efforts would have left many thinking that Benfica were going to win the first match of their Champions League campaign.
However, a second-half resurgence from Inter ensured that both sides shared the points at the Estadio da Luz.
Marko Arnautovic and Davide Frattesi scored in the first 15 minutes after the break to leave Benfica holding on for the win.
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Their hopes were crushed in the 72nd minute when Alexis Sanchez scored from the penalty spot to make it 3-3.
Benfica are now unable to progress to the Champions League last 16 and would need to thrash RB Leipzig for a Europa League spot.
Sitting second on 11 points is Inter, a club where Joao Mario spent five years during his career and went out on loan to West Ham in 2018.
He made 14 appearances for the Hammers and scored two goals, before heading back to Italy and then signing for Benfica in 2021.