Canterbury had more than their share of possession but with NSW halves Josh Reynolds and Trent Hodkinson missing and hooker Michael Ennis playing halfback, the home side struggled to click their attack into gear, especially close to the Eels' goalline.
Corey Thompson worked his way over out wide for the home side in the 44th minute to reduce the Eels' halftime lead to 10-4.
But from then on the Eels, who had won just four of 29 previous matches without Hayne, took charge as uncharacteristic errors and a heavy injury toll mounted for the Bulldogs.
Toutai scored his second in the 58th minute off a great offload from Pauli close to the line.
The massive forward backed that up again in the 67th minute when he slipped another classy pass to Ryan Morgan.
Morgan raced 50m, beating a series of Dogs defenders for his second four-pointer in the 75th minute to seal the win.
Thompson scored his second in a consolation effort for the Dogs in the 78th minute.
Hit hard by Origin commitments the Dogs have lost three in a row, after winning seven straight, and lost both David Klemmer (leg), Sam Perrett (knee) to first half injuries.
Manu Ma'u (arm) also left the game in the first stanza for the Eels.
The win was the Eels' eighth of the season and pushes them up to equal third on the NRL ladder.
- AAP
