The Japanese driver initially thought that there must be something wrong with his car before he realised that he was being teed up for a shot at the fastest lap.
Tsunoda was running in 10th place in the closing laps when a pitstop window opened up behind him, helped by the chasing Alex Albon having a track limits time penalty.
That gave the chance to have a free stop for soft tyres, and he duly bagged the fastest lap bonus point on the very last lap, while retaining his 10th place.
After the flag, the disqualifications of Lewis Hamilton and Charles Leclerc moved him up to eighth, earning him a total of five points on the day, and exactly doubling the Faenza team's total for the season.
"To be honest, I got a heart attack when I had to box," said Tsunoda. "Because I thought it was something like an issue from the engine.
"After I heard we go for fastest lap, okay, then I was relieved, but still a bit of pressure on, and we were able to still get the fastest lap, so it was good."
While the likes of Hamilton and Max Verstappen have often pursued fastest laps after late stops for fresh rubber, this was a novelty for Tsunoda.
"Yeah, probably first experience going for fastest lap in the last lap," he said.
"Super enjoyed it, obviously after a lot of managing tyres, straight into the quali mode, this was kind of thrilling, but at the same time I enjoyed it, the amount of grip I felt with low fuel is amazing.
"Obviously for myself it was 100%, from the engine it was not probably 100%, we weren't able to fully recharge the battery or whatever. But yeah, for myself at least 100% last push.
"Especially here, it's a physically demanding track. It's pretty hard, but just re-focus and actually be able to kind of improve quite a big, big chunk of time. So it was good."
Tsunoda said the result was a tribute to the team members who have helped to keep new parts coming to the car.
"Yeah, definitely, I think especially the people who work in the background in Faenza and Bicester and try to improve our package as much as much as possible race-by-race," he noted.
"We're making progress little by little, and definitely I felt we're getting closer towards P10.
"So if we look at this race still I had a bit of luck towards the end to score points. But anything can happen like this race. So we tried to be around P10 and get the points as much as possible race-by-race."
The result also moved AlphaTauri to within two points of Haas and six of Alfa Romeo in the constructors' table.
"One point is a big difference," said Tsunoda. "So well done to the team. Still four races to go, so we just maximise our package, and see how it goes."
