The Canadian moved from third to second with three laps to go and moved inside Sato to take the lead just a few meters (yards) from the finish line at the Anhembi street track.
Sato, coming off his first career victory two weeks ago in Long Beach, drove in too hard for the hairpin at the end of the long back straight and gave space for Hinchcliffe to get past.
''To win a race on the last corner of the last lap is one of the coolest feelings,'' Hinchcliffe said. ''To make a last-corner pass, that's something I'll remember for a long time. Takuma was making that race car really wide and he was defending the inside pretty well. He just outbroke himself just a little bit and I was able to do a high-low (pass) and got the win.''
Sato had successfully defended the lead from Hinchcliffe on two other occasions during the final laps but couldn't hang on at the end with older tires.
''I think I tried everything I could to defend,'' Sato said. ''I was really struggling on the grip the last laps. I really had to deal with a lot of things. The last few laps were great fun from a driver's point of view. It's a real pity that I lost it on the final lap of the race on the final corner.''
Despite losing the race, Sato leaves Brazil with the lead in the drivers' standings. American Marco Andretti, who finished third on Sunday, moved to second for the championship.
Helio Castroneves, who led coming into his home race, had an incident-filled race and finished 13th to drop to third in the championship.
Castroneves' Penske teammate Will Power, who won the previous three races in Brazil but started only 22nd after a mishap in qualifying, retired on lap 19 because of an apparent gear shift problem.
Andretti has had an unusually good start to the season on road and street circuits. It was the second third-place finish for him this year - he was also on the podium in St. Petersburg - and the result gives him some momentum going into the Indianapolis 500.
''I think right now we're on par for a great season,'' he said. ''This is what used to be the tough part of the season for me. We've been getting some decent results where I used to struggle, so I'm pleased with that.''
Spaniard Oriel Servia was fourth in the second-to-last race for Panther DRR racing, which will not compete after the Indy 500 because of financial difficulties.
American Josef Newgarden, who started last after changing an engine before the race, managed a fifth-place finish, the best of his career. Pole-sitter and current IndyCar champion Ryan Hunter-Reay ran up the front for a while but finished only 11th after a flat tire. Andretti teammate and front-row starter EJ Viso of Venezuela was sixth.
Tony Kanaan's impressive weekend despite an injured right hand ended in disappointment when he ran out of fuel before a pit stop on lap 51 while running second.
After stopping on top of the cross-finish line, he put both hands on top of his visor in disbelief as fans packing the stands at the Sambadrome front straight loudly applauded. He finished the race in 21st place, three laps back.
''I couldn't believe that something like that happened. I wanted to win this one for the fans really bad, they supported me all week,'' he said. ''It's tough, but it happens. I leave with my head up because I know that I did everything that I could.''
Kanaan came to Brazil not knowing whether he would handle the pain from the injury he sustained late in the Long Beach race two weeks ago, and battled through a sore and swollen right hand to qualify fourth on Saturday.
Power's winless streak was extended to 15 races after his disappointing weekend in Brazil. The ''King of Sao Paulo'' was the pre-race favorite after winning all three previous races at the Anhembi circuit. He dominated the first two practice sessions on Saturday, but a red flag kept him from posting a fast lap in qualifying.
Power didn't waste time moving up the field and had reached 11th place by Lap 18 before the mechanical failure ended his hopes of another victory.
''Obviously burned something with the gear shift because it stopped shifting, so I was looking for the automatic shift or the manual shift,'' he said. ''We don't know what happened, I had no real warning, unfortunately. I had such a good car. I was passing a car a lap.''
It was the first time Power failed to finish on a road or street circuit since the 2011 race in Toronto 2011.
The Australian came to Brazil in need of a good result after struggling in the first three races of the year, when he managed only one top-five finish.
Castroneves came boosted by the best start of his career after three straight top-10 finishes, but it was a difficult day for the Brazilian. He got involved in at least three crashes in the 75-lap race.
''We didn't have the race we wanted, everything happened to us,'' the three-time Indy 500 winner said. ''But we have to move on and think about Indy.''