Losing Sezer would be another significant blow for the Raiders.
Melbourne have already cemented a top-two spot, and whether Canberra or Cronulla will join them in hosting a home qualifying final in the first week of the playoffs will likely be decided in next week's matches.
Wests Tigers host Canberra at Leichhardt, while Cronulla travel to Melbourne. Soft defence from Manly allowed Paul Vaughan score the game's first try in the 10th minute. Rapana followed that up eight minutes later for a 12-0 lead.
The Trbojevic brothers then combined to get Manly back in the game.
Jake Trbojevic scored after Jack Wighton spilled a Matt Wright bomb. Tom Trbojevic then crossed out wide to peg the Raiders' lead to just two points.
Rapana's second try two minutes before the break gave the Raiders a 18-10 lead at the break. Edrick Lee and Jack Wighton also scored for the Raiders after halftime.
Rapana's third try with a minute to go sealed the win, but only after second-half tries to Tom Trbojevic (two), Daly Cherry-Evans and Frank Winterstein gave Manly a hope of an upset win.