Billy Slater scored a try in each half but his game lost some shine when he was put on report early in the second half for a swinging arm with Manly winger David Williams leaving the field with concussion.
Five-eighth Ben Hampton was also put on report for a lifting tackle on Tom Symonds.
The Storm were seething after video referees Ashley Klein and Ben Galea over-ruled referee Shayne Hayne to award a Manly try in the 26th minute.
Williams and Young Tonumaipea leapt high for a Daly Cherry-Evans kick with Williams appearing to knock the ball forward and Slater and Peta Hiku both scrambled to ground the ball.
Despite the footage being inconclusive that Hayne's initial decision was wrong, the video refs gave the green light to Manly.
The Storm hit back soon after when from a set play Ryan Hoffman popped a trademark off-load to Slater to level at 4-4.
They trailed 5-4 at halftime after a last-minute field goal from five-eighth Jack Littlejohn.
But they were first on the scoreboard after Slater ran on to a Hampton pass and beat Brett Stewart to touch down for this second four-pointer.
Just when it appeared the home side was building some momentum Manly hit back with a freaky effort from Jorge Tafua.
The winger somehow managed to plant the ball as he somersaulted over the sideline in a tackle by Sisa Waqa.
Four minutes later the lead was out to 19-10 when Jamie Buhrer caught the Storm napping as he charged from the back of the scrum to touch down and it looked like it would be Manly's game.
But Cronk somehow managed to kick a little grubber around Littlejohn, regathering to score before Mann's effort sealed the win.
-AAP