The reigning premiers scored five tries to three with winger Hazem El Masri posting a hat-trick, as part of a 22-point haul for the match.
He also added four conversions and one penalty goal.
Braith Anasta and Reni Maitua scored the Bulldogs' other tries while for the Eels, Dean Widders, Eric Grothe, Luke Burt crossed for four-pointers.
Burt kicked two conversions for the visitors.
El Masri opened the scoring in the 17th minute with his first try and it was not until close to half-time that the Eels provided a response through a try to Widders.
Burt kicked his first conversion of the night to give Parramatta a 6-4 lead, but the Bulldogs moved back in front in the 39th minute with a converted try to El Masri.
At the break the Bulldogs led 10-6 but it proved to be short-lived, as Grothe scored his four-pointer soon after play resumed with Burt adding the extras.
With the match evenly balanced at 12-10 in favour of Parramatta, neither side looked like taking control until Anasta crossed in the 49th minute for the Bulldogs.
El Masri kicked his second conversion to take a 16-12 lead and from this point in the match, the Bulldogs were never headed.
El Masri scored another converted try only minutes later and Maitua then crossed in the 62nd minute, with El Masri fourth conversion sending the Bulldogs well ahead.
The mercurial goal kicker added his penalty goal late in the match, before Burt improved the scoreline for Parramatta with his try only a minute out from full-time.
Bulldogs 30 (El Masri 3, Anasta, Maitua tries: El Masri 5 goals)
Eels 16 (Burt, Grothe, Widders tries: Burt 2 goals)