Navarro's eighth-inning line drive was originally ruled a three-base error, but the official scorer changed the call after talking to Brown postgame.
"I lost it in the lights," Brown said. "I would have taken it off my face if I could have, but I just couldn't see it. Our guy made a pitch to get out of that situation. I'm a little upset."
Starter Scott Kazmir (3-1) earned his third straight victory after allowing one run on four hits in seven innings. He struck out eight and walked one in his longest outing of the season.
"That was as good as we've seen Kaz this year and as good as he was in the second half of last year," manager Joe Maddon said. "He had great stuff and he pitched great."
Kazmir had his 16-inning scoreless streak snapped when Rajai Davis singled home Jack Cust in the fifth inning. But that was the lone hiccup in an otherwise outstanding effort.
"I felt good, but I still feel like I have a couple more steps to take," Kazmir said. "I feel like I'm not out there yet; I'm not extending my arm as much as I can and using my leg. But it was a great win. It's about time our luck changed a little bit."
Kazmir retired nine of the last 11 batters he faced.
"Every time I've seen him pitch, he's been tough," A's manager Bob Geren said. "He's one of the best pitchers in the American League."
Dan Wheeler, who gave up home runs in each of his last two outings in St. Louis, pitched a scoreless eighth and Troy Percival recorded his 13th save by pitching the ninth, but he allowed a solo home run to Frank Thomas.
"The bullpen had a bad stretch there in St. Louis, but they've been great here," Navarro said. "They just came back and did their jobs."
There was a moment of concern in the ninth when Percival grabbed his left leg after landing funny on a follow through.
"He slipped and felt it in his leg," Maddon said. "He was fine. He was throwing the ball great and said he wanted to stay in. In fact, he was adamant about it."
The Rays had runners on base in eight of the nine innings, including the leadoff hitter three times. They didn't take advantage until A's starter Greg Smith left the mound.
Jason Bartlett walked and Carl Crawford singled to open the eighth. Joey Devine replaced Smith and struck out B.J. Upton. Bartlett stole third and Crawford advanced to second on an error.
After Carlos Pena was walked intentionally, Evan Longoria was fooled on a breaking pitch and struck out on a check swing.
Navarro fought off a couple of pitches before punching the drive to left that all but hit Brown in the chest. The ball rolled to the wall, allowing all three runners to score easily.
"It just seems like we're a different team than in years past," Kazmir said. "A lot of things feel better when you're winning."
The Rays are 6-5 in their last 11 games in Oakland after losing their previous 11 in succession. They clinched their third series win in the last four trips here and can earn their first sweep in Oakland with a win on Wednesday.
The Rays own their best record after 46 games in franchise history. It is the first time Tampa Bay has won a 27th game before June 9.
"We're moving forward," Maddon said.