Bird left the field due to concussion and didn't return.
Cronulla totally dominated early, notching up eight points through a Luke Lewis try and a penalty goal and conversion to Maloney. It was nine and a half minutes before Manly touched the ball.
With Brett Stewart playing his first game of the year after overcoming a hamstring injury, Manly looked more threatening in attack.
The home side finally found their range in the 37th minute through hooker Matt Parcell, Jamie Lyon's conversion creating the halftime score of 8-6.
When Stewart scored his 87th try in 95 games at Brookie in the 48th minute Manly hit the front for the first time in the match.They pulled further ahead when Jake Trbojevic burrowed his way over from close range to lead 18-8.
Sharks winger Valentine Holmes had a quiet game, but he crossed out wide in the 65th minute to bring the visitors back into the contest.
But Tom Trbojevic shrugged off Ben Barba to join his brother on the tryscorers' list in the 73rd minute to seal the win for Manly.
Cronulla's poor record at Brookvale has extended to just five wins in 39 matches since 1967.
"It is great to get that first win, we have been disappointing the first two weeks," Barrett said.
"It was a relief to get the win, but it is a good feeling too."
Barrett admitted he was concerned about Taupau's tackle on Bird.
"A little bit, we will wait and see what happens," he said.
Cronulla coach Shane Flanagan said he expected the match review committee to take a close took at the incident.
"Jack didn't come back after that and the judiciary will take care of it," he said.
"It was a disappointing loss tonight. The effort was there but the execution wasn't. We just didn't take our chances."
The Trbojevic brothers led the way for Manly, while Andrew Fifita made 230m from 25 carries for the Sharks.
Flanagan said captain Paul Gallen was unlikely to be back for the Sharks' round four clash with Melbourne next Monday but should be right the week after.
Manly have a five-day turnaround before meeting the winless Sydney Roosters at Allianz Stadium on Saturday night.
- AAP