Keane was guilty of a careless handball that allowed Tom Huddlestone to put Hull ahead from the spot but he then displayed good skill to control Robbie Brady's corner on his chest before hammering home the equaliser.
A wholly forgettable first half had been enlivened momentarily five minutes before the break when Burnley's Ben Mee saw his goal-bound header juggled by Eldin Jakupovic on to the crossbar.
Yet despite having more of the play, Hull, who have now lost only one of their last 11 home matches in all competitions, were left frustrated and still in the relegation zone as the visitors hung on for a point after Ashley Barnes was sent off in stoppage time for a second yellow-card foul.
It was a first point on the road for Sean Dyche's Clarets since a draw at Manchester United in October.
(Reporting by Ian Chadband,; Editing by Neville Dalton)
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