Jacobs, playing up front, ran on to a through ball and placed it low and wide of the keeper but inside the posts to get Demons off to a great start.
Harris won the game in the closing stages with what coach and captain Yannis Kokkosis said would probably be their classiest goal of the season.
Harris took the ball to the left-wing byline and placed his left-footed shot between the goalkeeper and the near post, as if he were threading a needle.
He and Callum Innes had already scored a goal each as Wainui sought to consolidate their early advantage.
They led 2-0 but United pulled a goal back by halftime.
In the second half, United drew level.Wainui went ahead again, and again United equalised, this time 20 minutes from the end.
It was left to Harris and his precise shooting to secure the three points.
Kokkosis said that, apart from the goalscorers, Wainui were well served by Manaaki Terekia, who normally plays centreback but played left wing in the first half and goalkeeper in the second; rightback Ollie Suttor; central midfielder Aaron Welch, back from time away from the game; and Matt Tong, who fitted a football game into his schedule of snow-based leisure pursuits.
Tatapouri Bohemians are finding their football more enjoyable now they are back in what they consider their natural habitat — the second division.
They struggled in the early part of the season after being put in the higher of two divisions formed before the league was split again into three.
On Saturday, they lost 3-1 to another team who came down a level in the midseason makeover — Sunshine Brewing Wainui Salty Dogs.
Bohemians started well. They went 1-0 up in the first 10 minutes when Tom Paenga played a great ball from halfway over the top to right-winger Adam Situ, who took it on and slipped it past the oncoming keeper.
Salty Dogs equalised about the 20th minute and went ahead about the 35th.
Bohemians player-coach Chris Cockburn, who watched the action from the sideline on Saturday, said his side had a few chances to put themselves back in contention but couldn't quite finish them.
“We were a little flat in the first half, even after the goal,” he said.
“In the second half, we fought well. It was just unfortunate we didn't score a couple more goals and maybe equalise.”
Salty Dogs gave themselves a cushion midway through the second half with their third goal, and that ended the scoring for the match. The result leaves Tatapouri Bohemians third on the table.
Bohemians players to stand out were Situ, who played down the middle as well as wide on the right; Kapua Wharerau, who played on the left wing and down the middle; and rightback Luke Fisher, who had another good game.
Cockburn said Wainui were a classy side who held the ball up in midfield, played smartly through the middle and, once they were ready to go forward, attacked and could catch teams unawares.
Only one first division match was played last weekend — 1st Class Decorators Wainui Sharks beat Thistle Youth 8-1.
In other Eastern League 2 games, QRS Wairoa Athletic beat Smash Palace Shockers 2-1, and Thistle Vintage beat Gisborne Pro Roofing Bohemians 5-3.
In Eastern League 3, Gizzy Bobcat Services Thistle beat HES United Thirds 7-2 in the curtain-raiser to the Federation Cup game between United Prems and ALH Thistle (won 2-1 by United), and Ngatapa Silkies beat Tumu Thistle 2-1.
In the Women's Eastern League, the big showdown between Campion College and Gisborne Laundry Services Wainui Riverina ended in a 1-1 draw. HES United beat Tatapouri Marist Thistle 9-0.
Wainui top the table by three points, from Campion, who are six ahead of United.
