It was Brown's first goal in 13 games dating to March 30.
"It felt good," Brown said. "[Callahan and Kunitz] did all the work there. I kind of found the right area."
Tampa Bay took a 1-0 lead at 9:12 of the second period on a power-play goal by Namestnikov.
The Lightning went on the power play after defenseman Brandon Montour was called for hooking at 7:19.
Nikita Kucherov took a shot from just below the right face-off circle. Gibson stretched out his left pad and glove, but the puck hit his wrist and bounced out front. Ducks defenseman Sami Vatanen tried to sweep it back to Gibson but instead nudged it toward Namestnikov, who scored his ninth goal.
The Ducks went on their only power play at 10:27 of the third, and the NHL Situation Room initiated a video review of a shot by Montour at 10:48, but there was no evidence the puck crossed the goal line.
"I think everybody in the building would say it appeared to be in, but you have to have definitive proof," coach Randy Carlyle said. "That is the rule. Tonight was one of those nights it didn't go for us."
Gibson made 17 saves in the first period, including seven on Tampa Bay's two leading scorers, Kucherov and Steven Stamkos.
The Ducks were outshot 10-0 during a 7 1/2-minute stretch of the first period when Gibson made some of his best saves.
He slid to his left to turn aside a redirect from Kucherov at 9:15, denied a Stamkos backhand from in close at 13:29, and stuck out his right pad to block Stamkos' rebound attempt at 18:02.
"Our goalie held us in the first period," Ducks forward Corey Perry said. "He made some big saves for us. That wasn't the way to play a game against a team like that, but we found a way to claw back into the hockey game. A bounce here and there, it could go either way."
Tampa Bay had another prime scoring chance late in the first after Kucherov blocked a point shot from Anaheim defenseman Hampus Lindholm. The puck caromed out to center ice, and Kucherov had a clear breakaway but shot over the net with 18 seconds left.
The Lightning outshot the Ducks 37-29, including 17-7 in the first period and 12-7 in the second.
Vasilevskiy made 14 saves in the third, 10 after Brown's go-ahead goal.