Barrow saw off Kidderminster with all the action happening in the first half.
The Bluebirds scored three times in five minutes, with Adam Boyes curling home from the edge of the box and Andy Cook heading home Jack Mackreth's ball.
Dominic Rowe killed the game off with another curler before Harriers' Jamille Matt swept home Dean Lyness' long kick.
The hosts could have restored their three-goal lead when Michael Briscoe handled in the box but Lyness kept out Richie Baker's weak penalty.
VIEWS FROM THE DRESSING ROOM
Kidderminster manager Steve Burr told BBC Hereford and Worcester:
"Defensively as a unit we weren't at it and I thought they were very poor in the first half.
"These lads who have been in the side aren't grasping the chance and that is disappointing.
"Those who have been in the team haven't taken the opportunity so the sooner we get one or two back the better."