Bevan French started the contest indifferently, scoring the opening try down the right edge after three minutes after taking advantage of an overlap.
After 12 minutes the hosts for the day got on the board, James Tedesco breaking away near the middle of the field and outpacing the opposition to the right flank to level things up.
The Wests Tigers were next to post points when a penalty under the sticks allowed Tui Lolohea to make it 8-6.
Parramatta were having none of that - Semi Radradra scored out wide and the Eels took a 10-8 lead to the break.
More penalty goals had the Tigers in front - two in fact, had them up 12-10 by the 56th minute. Gutherson struck back for the Eels again, a 16-12 lead for the blue and gold at the hour mark.
Not laying down, the Tigers grabbed a try through Malakai Watene Zelezniak after a stunning aerial contest. Scores were level once more and it was down to whoever struck a better one-pointer.
Enter Corey Norman - slotting his first ever field goal after the Tigers produce an error via Jack Littlejohn to gift the Eels field position. A late attempt to level it up by Luke Brooks went wide and the Eels held on for a crucial win.
The Tigers now head to Cbus Super Stadium next Sunday to face an equally struggling Titans outfit, while the Eels stay at ANZ, hosting Brisbane on Friday night.