His feat was bettered by star fullback Billy Slater, who scored a hat-trick, with two in the second half as the Eels defence went to pieces.
Parramatta started well enough and were first on the scoreboard in the fourth minute.
They backed themselves and pushed the ball wide, with winger Semi Radradra touching down.
But that was all their fans had to cheer about as the Storm machine clicked into gear.
Five-eighth Brett Finch, who ended the game with a large, white bandage on his face after a cut, pulled the strings to set up both of Hoffman's tries.
It capped a big week for the veteran, who celebrated his birthday and announced his retirement at season's end.
The floodgates opened in the second half with Slater crossing twice, while youngsters Kenny Bromwich and Tim Glasby both scored their first tries in the NRL.
There will be celebrations in the Bromwich house, with older brother Jesse also scoring at the 73 minute mark to bring up the half century.
The Storm still weren't done with Will Chambers posting his second, while fellow centre Maurice Blair also deepened the misery for the Eels.