Boro stretched their unbeaten run to four games to collect a useful away point and maintain their play-off challenge.
Harriers rediscovered the art of defending after conceding nine goals in their previous two home games and fully deserved their point for a determined performance.
And manager Mark Yates will have been particularly pleased with the application of his players, after they soldiered on spiritedly without skipper Darryl Burgess after he was sent off with 18 minutes left.
Yates made four changes following the 5-0 midweek thrashing by Grays and was delighted with the way his reshaped line-up matched their high-flying visitors.
A swirling wind made it difficult for both sets of players and neither side could gain any superiority.
Chances were limited in the first period, but home keeper Dan Lewis had to pull off a tremendous save to turn a firm header from Luke Oliver on to his right-hand post in the 11th minute.
After the break it was the turn of his opposite number, Alan Julian, to earn the applause when he went full length to turn away a fierce effort from Jon Newby just after the hour mark.
In the 72nd minute Burgess got his marching orders when he was the last man and brought down Jon Nurse as he raced on to a flick from Darryn Stamp.
But Stevenage were unable to make the extra man count in the closing stages, although George Boyd came close with a well-struck volley that brought another fine stop from Lewis.