After a dynamic start, the host conceded successive tries, trailing 4-16 at the break and despite showing feisty form in the dying stages, lost the match 20-30 at Raemaru Park on Saturday.
The win sees defending champions Eels back to winning form after successive losses to Tupapa Panthers and Titikaveka Bulldogs in the earlier rounds.
Bears briefly led 4-0 before Eels scored three tries to lead comfortably 16-4 at the break.
The visitors continued their top form in the second spell to extend their lead to 26-4 before the Bears bounced back to score two tries in a brilliant fashion to cushion the deficit to 16-26.
However, a try in the corner was enough for the Eels to seal the win despite a late comeback from the Bears which sneaked in to end the match in a respectable 20-30 in favour of the Eels.
Veteran Billy Tuaivi was a key player for the Eels, barking orders on the field with help from other veterans Clive Nicholas and Terry Piri.
Lanky Lai Rogorogoivalu powered the backline with Sirla Pera, speedster Samu Alafua and Tua Ravula.
Newcomer Emori Nawasala also impressed, scoring a try in the win.
Rampaging Stan Tuaivi continued his barging runs, creating havoc for the Bears in the opening spell.
For Bears, season campaigners Steven Willis and Francis Smith stood out.
Their forwards put on a gutsy performance, making some hard tackles and determined runs to claw its way back into the game.
Basil Matapo proved instrumental for the side alongside Mau George, Luke Tukaroa and Turi Boaza.
Bears were let down by their poor handling, losing possession at crucial moments of the match.
Team official Pare Rongokea said simple mistakes cost them the match.
“We are our own enemy for today. We will go back to the drawing board to sort out how to cure our own wound,” he said after the match.
Eels mentor Albert Nicholas said they were happy to get back in winning form.
He hailed his players for standing their ground in the dying stages of the match.
However, Nicholas said there were still areas to work on before the second round which starts this weekend.
Meanwhile Bulldogs and Panthers also won the premier matches over the weekend.