The Hurricanes came out firing with Ruben Love scoring in the opening minutes before three tries in the final 11 minutes of the first half to Fineanganofo, Cam Roigard and Billy Proctor gave the visitors a 26-13 lead at the break.
The Reds struck back with two tries in the second half, before a second try to Fineanganofo sealed the win.
Hurricanes coach Clark Laidlaw said at this stage of the year they’ll take wins however they come.
“We know it’s a tough place to come win,” said Laidlaw.
“At this stage of the year, it’s not always about winning by more or looking for bonus points, it’s more about trying to win.
“I thought the composure and shot calling at the end to go to the corners and kill the game was encouraging. It was a tight battle and an enjoyable game.”
It was the Hurricanes’ fourth straight win, as they leapfrogged the Reds in the standings.
Finishing fourth is important, considering the new playoff format Super Rugby Pacific has adopted this season.
The finals format involves 1 v 6, 2 v 5 and 3 v 4, with the three winners and the highest-ranked loser advancing to the semifinals.
With the Crusaders, Brumbies, Chiefs and Hurricanes already confirmed for the playoffs, it leaves the Reds, Moana Pasifika, Blues and Waratahs to fight it out for the remaining two spots.
The Hurricanes host Moana Pasifika in Wellington next weekend, while the Reds are at home to the Fijian Drua.
Hurricanes 31 (Ruben Love, Fehi Fineanganofo 2, Cam Roigard, Billy Proctor, tries; Ruben Love 3 con)
Reds 27 (Tate McDermott 2, Joe Brial tries; Tom Lynagh 3 con, 2 pen)
HT: 26-13