Harriers who suffered a 6-1 defeat at the hands of their opponents in September, looked set for revenge in the return game.
They called all the shots after Simon Brown fired them ahead in the 22nd minute on his home debut.
But Hull City salvaged an important point in the 68th minute when Burgess netted his 16th goal of the season after a blunder by home defender Adrian Viveash.
Even then Kidderminster almost won it when John Williams clipped the crossbar with a rising drive in the 89th minute.
The result meant second placed Hull lost ground on leaders Doncaster who beat Bury 3-1 but it could have been worse for the the Tigers who were off-colour for the first hour.
Kidderminster looked determined to pull out the stops for their manager Jan Molby who was sacked by Hull towards the end of last season, and played the more inventive football from the start.
They got the break through after 22 minutes when Brown, on loan from West Bromwich Albion, netted a sweet goal on the run after being put through by Adam Murray.
It was his second goal in two games after he had marked his full debut by scoring for Lincoln the previous week.
Hull had already been rocked by the loss of defender Lee Marshall who was stretchered off with a suspected broken leg after a 12th minute collision with Scott Stamps.
Hull rarely showed the kind of form that has made them favourites to gain automatic promotion, although Stuart Green was unlucky with an 18 yard free kick that rattled the home cross bar in the 35th minute.
After the break Harriers keeper John Danby made a terrific one handed save to deny Stuart Elliott but the home side handed Hull a soft equaliser in the 68th minute.
Viveash wanted too long to size up a clearance deep in his own half. Elliott nipped in to pinch the ball before squaring for Burgess to rifle home.
Hull looked the most likely to win it from that point, although they were fortunate when Williams showed good skill to create some space and shoot against the bar just before the end.