City elected to bat first and were immediately on the back foot when Sam Walker (1 for 14) removed Matt Lobb for just two.
However experienced heads Joey Yovich (25) and Ian Page (28) held firm and put on a quick 33-run stand.
But Onerahi fought back in what would be the theme of the day with Sean Doel (1 for 6) and Kirk Henderson (1 for 9) removing the set batsmen.
Coutts (2 for 15) came on and grabbed two quick wickets with his medium pace to put City into a hole but Simon Fenwick's 19 helped pull them through to the 100 mark.
Onerahi captain Tom Herman (3 for 16) brought himself back on at the death and was rewarded for bowling a great length, taking a final over hat-trick which included two balls that uprooted the stumps.
With Onerahi needing just 101 to win, City needed to take quick wickets if they were to have any shot of winning the title.
They did just that with Kieran Nelson (2 for 21) and a classy piece of fielding from Harry Darkins reducing Onerahi to just 21 for 3.
Coutts was joined in the middle by Tom Keogh and the pair combined for the defining partnership of the match.
Both players rotated the strike well with Coutts' power and Keogh's ability on the drive frustrating the City attack.
The pair put on 60 runs for the fourth wicket before Keogh was bowled by Darkins for 21.
Coutts kept his head down and inched Onerahi closer to the target, taking particular liking to the bowling of Gary Paine. He struck a six and three fours in Paine's one over.
Coutts and Herman knocked off the last 20 runs required for victory with 29 balls remaining, sparking jubilant celebrations.
This put a bow on a top weekend for Onerahi, who took the last two wickets quickly to beat Kamo by an innings and 129 runs in the Oxford Trust Two Day competition.
It was Coutts again who led the way, taking 11 wickets for the match to go with a first innings 130 with the bat.
The man of the moment said he's never been in such a purple patch.
"Can't beat this kind of form really. The beers will flow now and we'll enjoy ourselves," he said.
In the other match, City claimed a first innings win over Westech Automotives Maungakaramea.
Maungakaramea had set City a target of 151 for first innings points after contributions from Tom Lovegrove (47) and Sean West (40).
City's top order provided the basis of their innings of 221, with Ian Page's 89 the standout innings.
Bert Horner and Quinn Pooley both added 32 to give them a 71-run buffer. West (4 for 43) was the pick of the bowlers.
Maungakaramea ended day two on 71 for 7 to deny City the outright win despite the best efforts of Nelson (4 for 28).
