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The Sea Eagles had been seven points down with seven minutes of normal time to go before beginning a late fightback.
Fullback Tom Trbojevic producing a chip-and-chase try from nothing, Matt Wright kicked the conversion and then Cherry-Evans landed a field goal to tie up the score with two minutes on the clock.
Warriors star Shaun Johnson and Cherry-Evans each had another go at a one-pointer in the final minute of normal time, but both went wide, before Cherry- Evans nailed the extra-time winner, kicking into the wind with his left foot after stepping off his right.
The result halted a Manly slump and maintained its play-off hopes, but for the Warriors, already out of finals reckoning, it was an eighth loss in a row.
Manly dominated the early stages in front of 9167 fans and was aided by a couple superb 40-20s from five-eighth Blake Green.
The second ended just outside the corner flag and led to lock Jake Trbojevic opening the scoring in the 13 minute.
Wright added the extras and then a penalty, before the Warriors struck back.
The home side had been guilty of some sloppy touches but then benefited from a Manly turnover deep in its own half to send winger David Fusitu’a over in the corner.
Eight minutes from halftime, Fusitu’a got his second chasing a Johnson kick into the in-goal.
While Warriors hooker Issac Luke had produced the break that led to that second try, he was not able to land the handy conversion to break the 8-8 deadlock.
After Wright added a penalty early in the second spell, Tom Trbojevic produced a piece of magic to help push Manly further ahead.
Given the ball on the halfway, he broke clear, dodged a tackle and produced a cross-kick that centre Dylan Walker latched on to to score.
Three minutes later, Fusitu’a came up with some skill of his own, snaring a Johnson attacking bomb and sending centre Blake Ayshford over, with Luke’s conversion levelling the score again with half an hour to go.
The home side did not lead until 10 minutes from the end when winger Ken Maumalo finished off an expansive move in the corner.
Johnson landed the sideline conversion and then a field goal, before Manly’s late charge.