It's the Auckland club's first National Rugby League win in four games and comes after four players returned to New Zealand this week to be with their families, ending their involvement in the competition.
Peta Hiku bagged a brace of tries while Tohu Harris scored the match winner.
The Warriors trailed by six points at half-time but two pieces of brilliance from Hiku on the left edge pushed the visitors ahead 20-14 after an hour.
Another try to Tohu Harris sealed the result for Todd Payten's men four minutes later, snapping a three-game losing streak in the process after a difficult month that included the departures of David Fusitu'a, Ken Maumalo and Agnatius Paasi.
Parramatta winger George Jennings deputised on the left edge in place of Maumalo and didn't look out of place, while Eels teammate Daniel Alvaro and Penrith loan prop Jack Hetherington also provided some much-needed power in the middle.
For the Wests Tigers, it was another case of letting slip a game they were expected to win.
Captain Roger Tuivasa-Scheck was again a leading figure for the Warriors despite a couple of early errors.