The resultant spot-kick was drilled home in emphatic style by 38-year-old Graham Alexander.
Burnley had further chances to increase their lead prior to half-time, but both Wade Elliott and Chris Eagles could not take the opportunities which were presented to them.
Hull started the second half far more strongly and took the game to the Clarets. The turning point and perhaps the deciding factor in Brown's future came when the referee disallowed a Geovanni goal from a free-kick for alleged pushing in the Burnley defensive wall.
The decision seemed extremely harsh and with it could have ended Brown's reign.
Things got worse when the influential Geovanni was shown a second yellow card and the game was finally put to bed by the home side when Alexander scored with a low shot from 20 yards to seal the three points.
Alexander was playing his 100th game for Burnley and his 900th game in a career which has lasted for 20 years. Where Tigers boss Brown goes from here will no doubt be decided in the next 48 hours.
The win for Owen Coyle's side takes them seven points clear of struggling Hull, but for long periods in the game there was little to choose between these two sides, who although showing plenty of endeavour and spirit lacked real quality overall.
Until his dismissal Geovanni was the most influential player on the field, but City couldn't find an end product to match his approach play.
Alexander's double strike takes his Premier League goal tally for the season to three and makes him Burnley's leading league goalscorer.