The Dragons showed their new penchant to chance their arm when they ignored an easy penalty goal attempt eight minutes after the restart - their adventure paying dividends when Soward grubbered for Brett Morris to score.
The red and whites could have put the issue beyond doubt when Matt Cooper finished off a nice interchange between Soward and Chase Stanley - but Soward missed a simple conversion.
It was all the invitation the Tigers needed, Ben Murdoch-Masila barging through three defenders to score before Robbie Farah and Braith Anasta put James Tedesco into open space and he found a flying Tim Moltzen in support.
Soward missed with his first field goal attempt which was touched in flight, but he made no mistake with his second shot from 20m out.
The Sea Eagles have moved to second on the ladder courtesy of their 25-18 win over Cronulla at Brookvale Oval yesterday.
The Sea Eagles dominated the opening exchanges to lead 16-0 through tries to Justin Horo, Daly Cherry-Evans and Tom Symonds.
Cronulla hit back through winger Nathan Stapleton each side of halftime to make it 16-12 after 48 minutes.
Then Manly found another gear. Peta Hiku crossed in the 59th minute and Steve Matai added a further try.
Stewart Mills replied for the Sharks with Chad Townsend converting from the sideline. But a Cherry-Evans field goal with five minutes to go sealed the victory for Manly.
Manly 25
Sharks 18
Dragons 13
Tigers 12
-AAP