Briscoe, who led a race-high 85 laps in the No. 6 Team Penske Dallara/Honda, dueled with Dario Franchitti over the last 50 laps before earning a second-place finish. The result kept Briscoe in the lead in the IndyCar Series championship standings, three points ahead of Franchitti, the race winner.
Meanwhile, Castroneves held on to a car that was tough to tame, finishing seventh to keep himself and the No. 3 Team Penske Dallara/Honda team in the thick of series points races.
Briscoe's runner-up effort was his third consecutive second-place finish, but it was far from easy.
"It took me awhile to find out where the car needed to be, but once I did, it was lightning quick," said Briscoe. "I had a great battle with Dario. Unfortunately, I didn't have enough for him at the end. I thought with the lapped traffic coming up I was going to be able to catch him like I did during the previous stint, but he actually got the luckier draw with the traffic and was able to extend the lead. It was tough, but it was a pretty good day to come in second and keep the points lead."
Castroneves, who started from the pole after a washout of qualifying Saturday put him in the No. 1 starting position based on entrant points, thought he might have been too cautious late in the race.
"We were struggling quite a bit, and you could see it toward the end," said Castroneves. "It was one of those things. I should have gone with my instinct, but because I'd finally gotten comfortable with old tires, I decided not to touch them. That was a mistake."
Briscoe's finish was Team Penske's eighth podium result in the first seven races this season.
"I felt like I left a little on the table coming in on the backstretch," said Briscoe. "It was the first time I'd really had a chance to practice coming into the pits under green. We missed the first practice session yesterday, and that's when you usually practice in and out laps."
Ever the optimist, Castroneves noted that both Team Penske drivers look strong in the championship race - Briscoe is leading and Castroneves is fourth, 29 points behind - and the Team Penske cars are first and second in the season entrant standings, which determine pit positions and starting positions in the event of qualifying cancellations, like Saturday's at Iowa Speedway.
"There's a bright side to everything," said Castroneves. "It wasn't the result we wanted, but we were able to get positive finishes out of it. Now it's on to Richmond to get a good result there."
The IndyCar Series returns to action next Saturday night, June 27, with the SunTrust Indy Challenge at Richmond International Raceway.