The Tigers opened the scoring after seven minutes through David Nofoaluma's eighth try of an excellent debut season.
However, Stuart's side responded well to that early setback with Ken Sio and the impressive Jake Mullaney crossing in quick succession.
Hayne played a role in both tries and his side should have extended their advantage when Roberts got his hands to Marshall grubber kick and broke free, only to produce an appalling pass to undo all of his good work and cough up the ball.
And just shy of the half-hour mark the Tigers regained the lead through the lightning-fast Marika Koroibete with Marshall adding the extras.
Toutai finished in the left corner after more good work from Hayne just before halftime, but after the break the Tigers came racing out of the blocks but were unable to score following three successive sets on the Eels' line.
Both sides struggled to keep hold of the ball on occasions, but the Tigers did finally add a third try when Koroibete, who scored four times against Parramatta last year, added his second 12 minutes after the restart.
But the Eels kept pressing and Joseph Paulo showed great strength to touch down just after the hour mark, only for the visitors to hit back through Simona.
A big run from Fuifui Moimoi set up a final push for the home side and Roberts showed brilliant footwork and vision to find Tautau who made no mistake with Paulo kicking the extra two points.
- AAP