A last gasp Robert Snodgrass free kick denied the Clarets after Steven Defour looked to have won it with a worldie!
Belgian international Defour struck 17 minutes from time with his first goal for the club, following a magnificent turn and run at goal from the half way line.
But with virtually the last kick of the game, Snodgrass struck to level matters and break Burnley hearts.
Clarets’ record signing Jeff Hendrick was named among the substitutes, after spending just two days training with his new team mates.
But there was a first start for Icelandic summer signing Johann Berg Gudmundsson, who replaced Scott Arfield.
However, it was a lively start from the visitors and Tom Heaton needed to be alert in the ninth minute to parry away an 18-yeard effort from Abel Hernandez, who looked to find the bottom corner with placement rather than power.
An almighty scramble from Burnley’s first corner, which saw two George Boyd shots blocked, signalled the hosts’ immediate intent.
And when Gudmundsson’s far post volley was deflected out into the path of Stephen Ward with 25 minutes on the clock, the Republic of Ireland full back’s audacious attempt from outside the box flew inches over.
But the closest either side came to scoring came right at the end of the half, when Snodgrass picked out David Meyler with a wonderfully–angled pass that the Irish international took in his stride and rifled across Heaton and against the outside of the post.
And from the restart, the Clarets had another let off when Adama Diomade side-footed Meyler’s low cross wide from six yards with the goal at his mercy.
The Clarets though began to grow in belief as the half progressed and Boyd tested Jakupovic with a drive from 25 yards, before Sam Vokes was off target from a similar distance.
Heaton again stood tall to turn over Snodgrass’s effort as Hull responded.
But with 17 minutes remaining Defour illuminated proceedings with a quite sensational strike.
A clever turn in midfield took him clear of his marker and the Belgian advanced and found the bottom corner with a stunning 25-yard bullet.
That was Defour’s last action as he made way for debutant Hendrick, with Arfield also replacing Gudmundsson.
Curtis Davies headed a corner off the roof of the bar as City looked for a response.
And just as it looked as though the Clarets had seen off the late assault, Ben Mee fouled Tom Huddlestone 25 yards out and Snodgrass curled home a beauty.
BURNLEY: Heaton, Lowton, M Keane, Mee, Ward, Gudmundsson (Arfield 75), Defour (Hendrick 75), Marney, Boyd, Vokes, Gray (Bamford 80).
Subs: Robinson, Kightly, Flanagan, Tarkowski
Booked: Mee 27, Arfield 82
HULL: Jakupovic, Robertson, Davies, Meyler (Mason 73), Huddlestone, Hernandez, Snodgrass, Clucas (Maloney 83), Livermore, Diomande (W Keane 71), Elmohamady.
Subs: Marshall, Maguire, Weir, Henriksen.
Ref: P Tierney
Att; 18,803 (1,399)