Peters' first-half blunder enabled lowly Harriers to complete a Conference double over the U's, who lost 2-0 at home to the struggling Worcestershire outfit last August.
Kidderminster, with only one win in eightleague outings, almost made a great start by creating a gilt-edged chance in the first minute.
A defence spliting pass Lee Thompson found striker Luke Reynolds, who ran in on goal before knocking the ball wide with only keeper Scott Howie to beat.
Cambridge however contributed to their downfall when under pressure Peters firmly headed into the back of his own net following a corner by Johnny Harkness.
A defensive mix-up in the 17th minute almost let in Craig Westcarr, but Kidderminster were worth their lead at the break.
The hard working U's however were much more threatening as an attacking force after the break, but were unable to penetrate Harriers' solid rearguard which was well served by Daryl Burgess.
Westcarr had a goalbound shot blocked and also put over a menacing cross which home keeper Dan Lewis dropped, before recovering in time to prevent Rob Wolleaston from capitalising on his error.
Cambridge sub Fola Onibuje had a header booted away in front of goal as Kidderminster battled to hang on to their slender advantage.
Harriers' only serious threat to the visitors goal during the second period was a long-range effort from Terry Fleming which was safely dealt with by Howie.