Gutherson starred with a hand in each of the Eels three first-half tries, before the Manly junior ran 50 metres for Parramatta's go-ahead try after the break.
Jake Arthur also set up two second-half tries, after enduring a tough opening half in defence as Manly cut the Eels' left-edge to shreds through Jason Saab.
The big margin came despite Manly leading 20-14 with 25 minutes to play, before Arthur stepped up and Parramatta ran in the last four tries.
It leaves the fight for the NRL's top-eight realistically down to nine teams, with Manly now needing a miracle to stay in the hunt.
With four rounds to play after this weekend, the Sea Eagles sit four points behind the eighth-placed South Sydney with a far inferior for-and-against record.
Parramatta are level on wins with fourth-placed Cronulla, eying off a second chance in the finals if they keep their winning ways.
The Eels' starting forwards in Junior Paulo and Reagan Campbell-Gillard were again dominant, while Shaun Lane threw offloads in the lead-up to two tries.
The match wasn't without controversy, with the Sea Eagles denied a penalty try early in the second half that would have put them 12 points up.
Chasing a loose ball to score, Morgan Harper was ruled to have shielded Will Penisini off the ball before claiming he had been held back on the way to the line.
But still, Manly only had themselves to blame after their late capitulation.
Parramatta started the better through two early tries to Maika Sivo, the first from a Gutherson cut-out ball and the next a grubberkick from the fullback.
Then after two weeks of drama, the Sea Eagles leapt back to life.
All three of their tries came through last week's boycotting players, with Tolu Koula, Christian Tuipolotu and Saab crossing and the latter breaking the line four times.Â
And at 20-14 ahead, Manly's season appeared to be reignited.
But two weeks after copping his own jeers from the Parramatta faithful, it was Arthur who stood up for the Eels.
He first laid on a sweet looping ball for Waqa Blake to pull off a superb flying finish.
And after Gutherson put the Eels ahead, it was Arthur who put the game beyond doubt with a grubberkick for Will Penisni with 11 minutes to play.
Dylan Brown also scored from inside his own end late in the match, giving Parramatta a much-needed for-and-against boost with their highest ever scoring total at Brookvale.
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