Tries to Maika Sivo and Dylan Brown in the first half enabled the Eels to take a 10-0 lead into the break, but the second period proved far more difficult for the visitors to put the Dragons away.
St George Illawarra lost winger Zac Lomax in the pre-game warm-up to a hamstring concern with Mikaele Ravalawa coming into the side in No.21 jersey as a replacement.
Ravalawa helped get the Dragons on the board in the 47th minute to narrow the visitors' lead after a Corey Norman cross-field kick fell back to James Graham, who helped send the Fijian flyer over in the corner.
The Dragons had an opportunity to level the scores with four repeat sets but an intercept from Michael Jennings, who struggled to show the speed he used to possess a decade ago, got the Eels out of jail under pressure.
Paul Vaughan had another interesting moment in a match, after last week's line drop out debacle, with the Dragons prop attempting to run off the field with a dislocated finger. He had reached out with his opposite hand to collar Clint Gutherson in space.
Vaughan was penalised for holding on too long before leaving the paddock to receive treatment as the Eels took the successful shot at goal for an eight-point advantage (12-4).
Vaughan wasn't having a great night. He was placed on report in the 50th minute for a crusher tackle on Nathan Brown.
An error from retiring forward Jeremy Latimore stopped another opportunity for the Dragons to strike back close to the line in front of 9,645 at the venue.
Mitchell Moses placed a well-timed cross field kick for Maika Sivo to clean up the scraps after opposite number Jason Saab couldn't contain the ball in the air.
The Eels extended their lead in the 22nd minute when Brown and Shaun Lane delivered late offloads to send Dylan Brown through the middle of the field before the Eels No.6 put the gas on to step outside Norman to the line.
Both sides have disciplinary concerns to come out of the clash with Euan Aitken (crusher), Manu Ma'u (dangerous tackle), and Kane Evans (dangerous tackle) all placed on report for alleged foul play alongside Vaughan.
An error from Clint Gutherson after points gave the Dragons another chance to level until a bumper hit from Dylan Brown on Tyson Frizell jolted the ball free.
Parramatta upped the ante late to secure their 11th win of the season and keep within reach of a top-four spot. But they lost their lock Nathan Brown to a knee complaint late in the clash.
Tensions boiled over with two minutes left on the clock after Evans' front-on tackle on his opposite prop Blake Lawrie. Evans was sin-binned as well as being put on with Lawrie leaving the field visibly distressed.
Dragons fans aren't feeling well either as that is their side's 13th loss for 2019, keeping them anchored in 14th spot. The Dragoins have also lost four of their past five games at Kogarah - which used to be a fortress for the Red V brigade.