The Grecians burst into a two goal lead inside 13 minutes thanks to a ninth minute opener from Steve Flack (pictured), followed by a Paul Buckle strike.
However, Kidderminster were not ready to lie down and they continued to fight and were eventually rewarded with a goal in the 87th minute from Dean Bennett, but Scott Stamps' dismissal in the last minute cost them any chance of a dramatic comeback.
Exeter held on for three valuable points which sees them climb to 19th place and out of immediate danger.
Halifax responded to the gauntlet by strolling to a 3-0 win over Barnet, who are hurtling down the division at an alarming rate.
Chris Clarke provided Town with a great start, with a goal in the 11th minute, but it took until the 70th until the game was made safe by Steve Kerrigan, which was followed by Michael Proctor hitting the third.
Darlington survived a nervy finish to complete a fantastic day for the strugglers of the league as they edged Scunthorpe United 2-1.
John Williams' double strike, after 37 and 74 minutes gave Darlo a 2-0 lead, only for an Alex Calvo-Garcia goal in the 84th minute to cause The Feethams' faithful a worrying final few minutes.
Elsewhere, Hartlepool continued their magnificent run and eased to a 2-0 win at Plymouth, their 19th game in a row without defeat.
Tommy Miller set them on their way with a 28th minute effort and Tony Lormor completed the scoring three minutes from the interval.
The win keeps them in fourth, but Blackpool, one place behind them, fell to a 2-1 away defeat at Macclesfield Town.
Two goals in six minutes gave The Silkmen a dream start as Richard Tracey (22) and Atkins scored for the home side.
Steve McMahon's side continued to plug away and got a consolation in the 86th minute from Richard Walker, but could not force the winner.
The top-of-the-table game between Brighton and Chesterfield was called off because of a waterlogged pitch.
Click below for the relevant report when available:
Darlington 2 Scunthorpe United 1
Exeter City 2 Kidderminster Harriers 1
Halifax Town 3 Barnet 0
Leyton Orient 1 York City 1
Macclesfield Town 2 Blackpool 1
Plymouth Argyle 0 Hartlepool United 2
