Two tries in the opening 20 minutes from Chris Lawrence laid the foundations for the Tigers, as the Eels twice coughed up the ball deep in their own half.
With the newly re-signed Robbie Farah and Benji Marshall dominating, the Eels could not get a foothold on the game and they didn't help their cause by giving away needless penalties.
The visitors were made to pay on the half-hour mark when Blake Ayshford darted over in the right corner, boosting his side to an 18-0 halftime lead.
Parramatta's Ryan Morgan gave his side hope three minutes after the restart when he crossed for their opening try, but the hosts were quick to respond.
Marshall and Tim Moltzen scored the Tigers' fourth and fifth tries in the space of three minutes.
Vai Toutai and Jacob Loko touched down to make the scoreboard more respectable for the Eels, but Jacob Miller put their hopes of victory to bed with a field goal in the 74th minute.
Mitchell Allgood and Jarryd Hayne were both guilty of losing possession early and the hosts took full advantage, twice spreading the ball to the left where Lawrence muscled his way past Chris Sandow to score.
The Eels almost reduced the deficit on the stroke of halftime when Hayne made a great break down the left wing.
He released Vai Toutau, who in turn found Loko, but the young centre, under pressure from Farah, came up with another handling error and butchered the chance to score just in front of the line.
Tigers coach Mick Potter was full of praise for his side's first-half performance, and revealed it was a tactic to target the diminutive Chris Sandow.
Lawrence scored twice in the first half when he ran over Sandow and Potter was pleased to see the plan come off.
"You can get that with smaller defenders and we recognise that," he said.
"Chris did very well to get over him."
Skipper Robbie Farah said the Tigers were improving slowly but still had a long way to go.
"We're getting better but we are not where we want to be," he said.
"But we are heading in the right direction."
Eels coach Ricky Stuart said his side would learn from the mistakes they made during the game and that the lack of possession in the first half really hurt them.
"When you start a game like that with the other team having 70 per cent possession to our 30 it is always going to be hard," he said.
"At one stage we had to defend 16 plays on our line but our defence held firm which was encouraging."