The victory, secured by Bailey Hobson’s hat-trick, sets up a third round trip to Curzon Ashton just before Christmas and was a welcome result after three straight league defeats in the previous weeks.
Heath now hopes it will provide a springboard to picking up more points in the National League North.
He said: “It was a cup game and it’s important to get a result.
"The players were magnificent. We’ve had a really difficult week in losing Elliott Reeves before the Southport game and then we lost Yousefu Ceesay on Thursday and suddenly were really stretched.
"So recalled young Harvey Grice who did ever so well when he came on and the players both played the conditions and did the basics really well.
"We knew we’d get our opportunities in the second-half and we took them.
"We needed that win. The defeat to Gateshead was gutting for us as we could have won that game, then we came across a really good Kidderminster side and after that were really disappointing on what was a horrid Tuesday night trip to Southport.
"But we’ve reacted well, the lads have rolled their sleeves up and the players that came back in were outstanding and defensively we were collectively solid.”
The Reds now head for a league fixture at Curzon Ashton on Saturday, two weeks before their FA Trophy clash.