They clinched a well deserved victory thanks to first half goals from Yusifu Ceesay, Krystian Pearce and Ethan Freemantle.
Aggborough boss Russ Penn’s side, who were in seventh spot before kick-off, are now unbeaten in their last four outings.
Harriers were unchanged from the team which triumphed 1-0 at home to Tamworth in the second qualifying round of the FA Cup the previous Saturday.
Striker Amari Morgan-Smith, a substitute against the Lambs, was unavailable due to injury while forward Jack Bearne, yet to make his debut following a season long loan move from Liverpool, just narrowly missed out on coming off the casualty list.
Harriers made a lively start and raced into the lead in the tenth minute when Ceesay fired a neatly struck shot past goalkeeper Cameron Gregory, a former Kidderminster loanee.
It was his first goal for the club in his ninth appearance.
Harriers continued to push forward and confidently stretched their lead in the 18th minute when defender Pearce finished off a corner for his second goal of the campaign.
The Poppies regularly had to be on the guard in defence and visiting front-runner Freemantle managed to get in a shot which was smartly dealt with by Gregory.
Kettering gradually started to a flicker of improvement and forced a couple of corners shortly after the half hour mark, but both came to nothing.
Harriers, however, made it 3-0 on the stroke of half time when leading scorer Freemantle notched his fourth goal of the season with a smart shot on the turn from close range.
The hosts had a good chance to reduce the deficit early in the second period, but Brad Gascoigne fluffed the opportunity by heading into the ground and over the bar.
Gascoigne was guilty of another costly miss shortly afterwards when he failed to hit the target with a curling close range effort.
Both wasted chances, however, failed to unsettle Harriers who comfortably went on to seal their third away victory of the season.
Kidderminster: Palmer; Foulkes (Lissmore, 90), Pearce, Knight-Percival, Richards; Byrne, Brown (Rogers, 87); Cessay (Margetson, 80), Hemmings, Martin; Freemantle. Subs not used: Leak, Hewett.
Referee: Richie Watkins.