Luck didn't favour them at the start of the second half, with the Parramatta kick-off bouncing between the legs of Cowboys second-rower Ethan Lowe.
That allowed Brad Takairangi the opportunity to cross, but the centre could not control the ball over the line.
It took seven minutes for the Cowboys to find some attacking possession in the second half, and bench hooker Rory Kostjasyn took full advantage, scoring his first try for 2015.
Taumalolo found his second in the 60th minute, Johnathan Thurston's conversion pushing the lead out to 18.
That crushed the Eels' resolve, and as prop Darcy Lussick wrestled with Cowboy Matthew Wright, hooker Jake Granville scooted clear to put Kane Linnett over to push the margin out to 24.
Minutes later, Granville cashed in with a try as the Cowboys continued to carve the hapless Eels up.
Lachlan Coote and Wright completed the rout with tries in the final five minutes.
- AAP