In the end, they were undone by their own errors and Manly's superior attacking skills although this as far from an 80-minute performance from the Sea Eagles.
Second-placed Manly started as clear favourite after a runaway 38-6 win over the struggling Roosters and 10 wins from their last 12 games.
The Eels were in a much different head space after their 56-6 thrashing by the Rabbitohs last week, their ninth loss in their last 10 matches as they languished just one point ahead of the cellar-dwelling Titans.
Kiwis coach Stephen Kearney, who has had such a difficult season with the Eels, resisted the temptation to wield the axe but Parramatta went into the game low on confidence. Anthony Watmough was making his 200th appearance for the Sea Eagles, and Des Hasler was having his 200th game as coach, but that did not translate into a strong start.
Instead, they trailed 0-10 after the first quarter, the Eels scoring the first try through Chris Hicks when Steve Matai threw a wild pass from dummy half which eluded everyone. Cherry-Evans started and finished off a try for the Sea Eagles but the Eels took a 14-6 lead into halftime when Ryan Morgan scored after quick hands by Burt.
The Eels' lead was deserved. They were unrecognisable from the rabble of the previous week but the Sea Eagles were uncharacteristically sluggish and Hasler, who ripped the dressing room door off its hinges on his last visit to the ground, must have felt like doing the same.
There was more urgency and aggression about Manly in the second spell and they took the lead for the first time, 18-14, after 10 minutes after two tries by Matai, both off Parramatta mistakes - the first a wayward pass by Jarryd Hayne and the second when the spinning ball eluded Hicks in-goal.
It became 20 points in 20 minutes for Manly when Brett Stewart finished off an 80-metre try started by a jinking run by Cherry-Evans and a draw and pass from Jamie Lyon. Justin Horo scored a late try for the Eels.
Eels 20 (C. Hicks, R. Morgan , J. Horo tries, L. Burt 4 goals)
Sea Eagles 26 ( D. Cherry-Evans, S. Matai, 2, B. Stewart tries, J. Lyon 5 goals)
Halftime Eels 14-6.
In last night's other late game, the table-topping Melbourne Storm dispatched wooden spoon favourites Gold Coast with ease, winning 40-16.
Storm 40 (C. Cronk 3, B. Slater 2, S. Manu, A. Quinn tries; C Smith 6 goals)
Titans 16 (D. Moore, B. Thompson, W. Zillman tries; P Campbell 2 goals).