Redmond kept out Phil Edwards' header in the 16th minute and did even better to deny Kee with an instinctive one-handed save just after the half-hour mark.
Edwards then went close with another header from Luke Joyce's corner.
However, Kee made the breakthrough on the stroke of half time when he headed home Sean McConville's cross from eight yards out. There was little that Redmond could have done.
Stanley continued to control the game after the interval and were rewarded in the 76th minute when Symes side-footed in another Joyce corner.