Power had a lap of 1 minute, 21.4045 seconds on the 2.5-mile, 11-turn Anhembi circuit on the streets of South America's biggest city, less than half a tenth of a second ahead of Franchitti. Scott Dixon, Franchitti's Chip Ganassi Racing teammate, will start third.
It was Power's second pole of the season and second consecutive in Sao Paulo. His lap on Saturday eclipsed the previous qualifying record at the track.
"It was a good run," Power said. "They were telling me it was going to be close. It's satisfying when you get pole by such a small margin because you have to rag it so much to do that. It seems like very tough, close competition, which is typical of IndyCar. We're just giving ourselves the best opportunity for the first corner."
Power is trying to win his third straight race in Sao Paulo. The Australian also won the last two races heading into Brazil and is the series points leader. He will try to give Penske its fourth straight win to start the season for the first time in team history in IndyCar. The team has already won every pole this year.
Franchitti had been fastest in Saturday's practice, but made a mistake in qualifying that he said was costly.
"The car is very good," he said. "I'm a little disappointed with myself, on that last lap I made a mistake."
He added: "You have to congratulate Will, he put it together, he did the lap. I'm happy that I feel the time is in the car and we can adjust it for a good race car tomorrow. It's a good position to be in second. Feels a lot better than in the first three races."
Franchitti won the last three series titles but struggled at the start of the season, not finishing better than 10th.
Qualifying was run under overcast skies but dry conditions. Rain affected the first two races won by Power in Brazil. The inaugural event was postponed for a day and last year the race was cut short.
"It's wet tomorrow, obviously that's going to change everything," Power said. "It's not the average race. There are always position changing and different strategies, so we'll see how it plays out and we'll adjust accordingly."
Some of the main changes to the track this year aimed to improve the drainage system at the street circuit. Officials also reduced a strong bump near the braking point for the first chicane, which drivers had complained about last year.
"It is much better now, they were able to fix that," said Helio Castroneves, who qualified only 20th for his home race after crashing during practice earlier in the day.
It was the first time the cars were able to race after Honda was allowed to make changes to the turbochargers on its engines, giving the six teams using them an extra boost of power. Honda was permitted to make the change after a three-person panel on Thursday upheld an IndyCar decision against an appeal by Chevrolet.
"That helped as well," Franchitti said about the engine change.
Power got the pole with Chevrolet in his Penske, but six drivers using Honda engines will start in the top 10 on Sunday.
"Now they do have an advantage on us," Power said.
Lotus also is supplying engines to teams this season. IndyCar has multiple engine manufacturers for the first time in seven years.
The best Brazilian driver was Tony Kanaan, who will start 12th. Kanaan's KV Racing teammate Rubens Barrichello, in his first race at home since joining IndyCar this season after a 19-year career in Formula One, will be just behind in 13th place.
"We are getting close," Barrichello said. "I thought we were going to have a chance to start closer to the front here, it didn't work, but we are improving."
Hinchcliffe was the only driver to make the Fast Six through all four races so far, and he also finished in the top six every time this year.
"We're steadily improving and if we can keep that trend up for the race we're looking good," he said.