But his compatriot Eto Nabuli scored for the Dragons with 12 minutes to go to set up a grandstand finish before 15,046 fans.
But Parramatta held firm thanks to some stoic goal line defence and some wasteful playmaking from Benji Marshall to hand the Dragons three straight defeats.
Euan Aitken scored the game's first try in just the second minute after Dylan Farrell chased down a Benji Marshall chip kick and passed on to his centre for the visitors to lead 6-0 with Gareth Widdop's conversion.
But Radradra's reply was swift, when he crossed for his first after Leeson Ah Mau spilt the Steeden from the restart to hand the Eels possession.
Chris Sandow's first sideline conversion of the night tied up the scores at 6-all.
After the blitzkrieg start, the only other points scored in the opening stanza were from a Widdop penalty goal in the 32nd minute.
Both sides did go close though with Eels pivot Luke Kelly held up by Joel Thompson in the 36th minute.
The Dragons were denied three times by the video referee, most notably in the 12th minute when a Dylan Farrell try was called back for obstruction when Chris Sandow fell down easily in the defensive line.
Those tryscoring woes, the joint venture's Achilles heel all year, continued after the break with Nabuli's effort the only one from the Dragons to trouble the scorers after halftime
Anthony Watmough was put on report for a first half high tackle on Ben Creagh.
Dragon Mike Cooper (back) and Eel Tepai Moeroa (shoulder) both suffered first half injuries but played on after the break.
The win moved the Eels two points above Newcastle, Wests Tigers and Manly, who all sit equal last on the premiership ladder.
Dragons coach Paul McGregor took issue with several calls that went against his side.
"It's disappointing," he said.
"I have been going through the correct channels for the past few weeks and I'll keeping doing that.
"(But) I don't think we played very intelligently tonight."
Eels coach Brad Arthur said he hoped their win over Melbourne two weeks ago before the bye was a turning point in their season.
The win over the Dragons marked the first time the Eels have notched back-to-back wins this season.
"We drew a line in the sand and said `enough's enough' after the Melbourne game," Arthur said.
"The boys got together during the week and had a little chat and I think it showed tonight."
- AAP
