After the Cowboys missed five field goals in regulation and extra time, Cherry-Evans stood up in the first half of golden point to nail a shot from 30 metres out.
The win moved the Sea Eagles into seventh spot on the NRL ladder after a Townsville clash between two sides jostling for finals positions.
Manly welcomed back Tom Trbojevic, playing at centre, with the 2021 Dally M medallist having limited involvement in his first game in eight weeks.
But while all the pre-match focus was on Trbojevic, Cherry-Evans was the star.
Manly had led the game 18-6 via a Jason Saab hat-trick before the winger limped off with an apparent calf injury and the Cowboys fought back to 18-18.
Jason Saab scored a hat-trick for Manly but left the field with what looked like a calf injury. (Scott Radford-Chisholm/AAP PHOTOS)
Cherry-Evans' first game-changing moment came when he skipped out of dummy-half with eight minutes to play, earning a penalty when pulled back after passing.
The Sea Eagles went 20-18 in front on the next set, after Jeremiah Nanai was penalised for interference in the ruck.
But North Queensland were back level when Scott Drinkwater slotted a two-point field goal from 43 metres out with three minutes left on the clock.
Cherry-Evans had a chance to win it for the Sea Eagles but sprayed a shot wide, before Chad Townsend missed three for North Queensland before fulltime.
The Cowboys had two more chances in golden point, only for Valentine Holmes to miss both.
But Cherry-Evans would not be denied twice, kicking his seventh golden-point field goal - three more than any other player.
Influential throughout, Cherry-Evans had set up Manly's first try of the night with a delayed pass for Saab in the second minute.
Saab's next came when he spun over and he added his third shortly after halftime, before the Cowboys took control of the game.
Townsend, after 12 minutes, scored a try for the hosts, while Reuben Cotter was particularly strong, busting through Haumole Olakau'atu for a 51st-minute effort.
Three minutes later Kyle Feldt added the Cowboys' third try of the evening.
Jason Taumalolo continued his resurgence and was clearly the Cowboys' best forward with strong stints in each half.
For Manly, a question hovers over how to eventually return Trbojevic to fullback.
He got through unscathed at left centre but had 13 runs for 70 metres, while also adjusting to the position in defence.
But stand-in No.1 Tolu Koula again starred at the back.
He finished with 298 metres and seven tackle busts, setting up a second-half try when he broke down field and put Saab over for his third.
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