With the win, Castroneves climbed up to second in the IndyCar championship standings, 19 points behind Power.
"We are on it. We are not playing around," Castroneves said after his win in Detroit.
The series will race at Texas on Saturday night. It is the second oval event of the season.
Two weeks ago, Castroneves came up 0.06 seconds short of winning the Indianapolis 500. He was attempting to win the Indy 500 for a record-tying fourth time. Ryan Hunter-Reay won it for the first time in his career.
Castroneves followed up from his second-place finish at Indianapolis with a fifth-place run in the first race in Detroit. He started on the pole and led the most laps in race 1 with 30. Castroneves is hoping his momentum will continue at Texas.
"I'm very confident with my team," he said. "The Hitachi car, we know what we got, especially after Indy. Ovals, we've improved quite a lot."
Castroneves won an IndyCar race at Texas for a record fourth time last year. He grabbed the lead on lap 97 and then ran in front for the remaining 132 laps. His other wins at this 1.5-mile oval came in 2004, '06 and '09.
"Wow, I've won there four times," Castroneves said. "I guess Texas has been good to me."
Castroneves has yet to win an IndyCar championship. Last year, he held the points lead for most of the season but ended up losing the title to Scott Dixon by 27 points.
"[Castroneves] is just very strong. The guy has passion for winning and motorsports itself, which this sport is very tough on you," said Power, who took over the points lead after winning race 1 in Detroit. "A guy like him that hasn't won a championship, he's been so close. He'll be a contender this year. To me, he's better than when I first turned up on the scene."
On Friday morning, Tony Kanaan led the way in the first practice session at Texas. Kanaan, who is driving the No. 10 car for Chip Ganassi Racing this season, posted a lap at 219.382 mph. Dixon was second quickest, followed by Ryan Briscoe, Marco Andretti and Castroneves.
Twenty-two teams are on the entry list for the Firestone 600.
Series: Verizon IndyCar. Date: Saturday, June 7. Race: Firestone 600. Site: Texas Motor Speedway. Track: 1.5-mile oval. Start Time: 8:45 p.m. ET. Laps: 248. Miles: 372 (600 kilometers). 2013 Winner: Helio Castroneves. Television: NBC Sports Network. Radio: IMS Radio Network/SIRIUS XM Satellite.