However, Andrew Leering’s team had first to work extremely hard to dislodge the home side’s tenth wicket pair Chris Steele and Alex Rennie who survived 18 overs before Freddie Fowler finally ended their draw hopes with nine balls remaining.
Harrison smashed 86 from only 46 balls and with Harry Johnson and Josh Baker also compiling rapid-fire half-centuries the visitors piled up 325 for nine in their 55 overs.
Kidderminster were then in total disarray at 95 for nine in the face of fine spells from a youthful visiting seam attack plus Worcestershire slow left-armer Baker before their tenth-wicket pair dug in to good effect.
They defied everything Wardens threw at them to add 68 runs and survive for over an hour before Fowler’s late intervention clinched the spoils for a visiting side who in the process completed a seasonal double over Kidderminster and moved to second place in the table after 15 rounds of action.
“They almost managed to cling on so it was a very good win for us in the end,” Leering said.
“We dropped a couple of catches which made us slightly nervous but eventually a barrage of short balls did the trick.
“Our seamers all bowled very well and in particular Freddie Fowler bowled quickly on debut and thoroughly deserved his three wickets.
“We batted really well again led by another incredible knock from Jamie Harrison. He has missed a few weeks with an injury but you never would have known it.
“Josh Baker also used his long levers well to hit some sixes late on and get us past 300 for the fourth or fifth time this season.”
After opting to take first use of the traditionally run-filled Chester Road pitch, Wardens made the worst possible start when the in-form Henry Cullen was dismissed by the second ball of the match.
This brought Jacob Bethell to the crease and with Harrison quickly into his stride the visitors raced to 74 in only 6.4 overs before the Warwickshire all-rounder fell for 19.
Harrison was then joined by Pakistani pro Ali Zaryab (36) in a 55-run third wicket partnership which ended when the left-handed opener fell for a power-packed 86 which featured eight fours and six sixes.
Harry Johnson played the dominant hand in the middle part of the innings while making a 71-ball 62 but a good spell from home off-spinner Matt Pardoe (4-65) saw wickets fell steadily at the other end as the visitors slipped to 240 for seven.
However, the arrival of Pears all-rounder Baker quickly took the game away from the hosts as he blasted six sixes and three fours in an electrifying 35-ball 60.
With skipper Leering playing a supporting role, the eighth-wicket pair added 80 in only 45 balls before Tommy Rex added icing to Wardens’ cake with a breezy unbeaten 28.
This left Kidderminster chasing 325 but an hour later they had slumped to 45 for seven against a three-pronged visiting seam attack in which Rex (2-57), Fowler (3-26) and Hugo Whitlock (3-32) shared the early wickets.
Sinel Gunarathne made 30 from the top of the list and Charlie Stainforth contributed a useful 67-ball 40 from the middle-order, but when Baker claimed two quick scalps it was all down to Kiddy’s last pair.
And with the experienced Chris Steele, who made an unbeaten 86-ball 42, leading the way it was only when Fowler’s return induced Rennie (26) to edge behind that the visitors could end a nervy hour by celebrating a maximum 24-point return.