United deserved their 2-1 halftime lead, having played good possession football while controlling the tempo of the game. But they had struggled to penetrate a determined Rangers defence.
In the second half, United were more assured going forward and continued to dominate possession.
In the 55th minute, right-sided striker Sam Royston received the ball, beat a player and cut in along the edge of the penalty area. Just inside the box he let fly with a right-footed shot that went in at the top right-hand corner.
Twenty minutes from the end, Harris made it 4-1 when he made a run infield to collect a pass, beat two players and from just inside the box hit a shot that went in at the bottom right-hand corner.
Rangers scored a consolation goal two minutes from time. A ball came in from the Rangers left flank and, as two players went for it, they were both wrongfooted and the ball beat everyone on its way into the net.
United player-coach Kieran Venema's main concern after the match was a groin injury to Harris late in the game.
Venema said he would talk to Harris about the injury with a view to resting him this weekend, when United are scheduled to play Napier Marist Reserves in Gisborne.
The Marist first team will not be playing on Saturday, so the side coming to play United could be bolstered by first teamers.
Nevertheless, United would still be favourites and it is understandable that Venema would want to give Harris a rest now to get him right for crunch games in later weeks.
Venema named rightback Adam Simpson as United's man of the match against Rangers. He defended well and when he went forward his distribution was good.
Corey Adams had another outstanding game, creating opportunities for others and getting on the scoresheet himself.
Centreback Mal Scammell and leftback Malcolm Marfell also shone.
Venema started and finished the game in a holding midfield role. It was his first full 90 minutes of football since last year, injury having affected the early part of his season.