The Italian, at the age of 18 years and 224 days, led for 10 laps in a 31-lap first stint on medium tyres after others had pitted and then set a best time of one minute 30.965 seconds on the hard tyres around the Suzuka circuit.
Antonelli finished one place ahead of seven-time world champion Lewis Hamilton, whose place at Brackley he took when the 40-year-old Briton joined Ferrari, for his third scoring finish in three races.
"It was not bad. What I'm most happy about today is the confidence I had in the car and the confidence to push, which I didn't have on Friday and the start of Saturday," Antonelli, who had struggled in practice, told Sky Sports television.
"It was quite surprising to get the fastest lap, but definitely the feeling I had in the car is the most important... I was able to explore the limit and to push and to play with the car as well.
"It's good learning and good experience for next time."
Antonelli was able to put in consistent lap times, with the pace improving in free air as he ran longer on the opening stint and was catching the cars ahead before he ran out of time.
"It was also a nice feeling to lead the race for a few laps and become the youngest driver in F1 history to have done so. The next goal is to do that on the only lap that matters: the final one," he said.
The previous fastest lap setter was Max Verstappen, with Red Bull in Brazil in 2016 at the age of 19 years and 44 days.
Verstappen, race winner for Red Bull from pole position on Sunday, still holds the record for the youngest ever winner at 18 years and 228 days, and Suzuka was Antonelli's last chance to beat that.