Michael Keane was the pivotal figure at both ends as the Clarets came from behind to stop the rot away from home and climb another place up the Premier League table.
Burnley had lost seven times in a row on the road since securing their only previous point away from Turf Moor at Manchester United in October.
But Sean Dyche's men doubled that tally as they showed great character to hit back and earn a deserved draw which lifted them to 11th-place - still 10 points clear of the relegation places - as they saw out stoppage time with 10 men following the late dismissal of Ashley Barnes.
Hull's revival under Marco Silva looked as though it might be about to continue when Keane was penalised for handball and Tom Huddlestone made it 1-0 from the penalty spot with just 18 minutes to go.
But the Clarets' defender responded superbly to that setback to score the equaliser himself just four minutes later with a top-class finish to keep Burnley heading in the right direction and the Tigers in the bottom three.
The KCOM Stadium had been a happy hunting ground for the Clarets with wins there in each of their last two Premier League campaigns.
A return to Humberside also meant Robbie Brady and George Boyd facing their former club and the ex-Hull pair were both prominent in a positive start for the Clarets.
Boyd tested Eldin Jakupovic with a low drive early on, which the City keeper saved low down to his left.
And the quality in Brady's left foot was evident as he supplied two dangerous balls into the penalty area which had the home defence at full stretch.
Boyd then set up Brady for a shot the winger sliced wide but Dyche's men couldn't force the breakthrough and Hull, having lost just one of their previous 10 home games, began to pose a threat as they grew into the contest.
Dieumerci Mbokani headed wide under pressure from the excellent Matt Lowton and after the big striker had again caused problems, former Burnley transfer target Kamil Grosicki lifted an attempted lob too high and over the target.
Burnley responded with Ben Mee meeting another accurately delivered Brady free-kick with a powerful header which Jakupovic palmed away with the help of the crossbar.
But Hull were presented with a set-piece of their own five minutes before the break following a pull by Ashley Westwood on Huddlestone, which saw former Rennes winger Grosicki fire a fierce 30-yarder just over the Burnley bar as the stalemate continued, Ahmed Elmohamady heading wide the last chance of the half from another Grosicki cross in stoppage time.
Tom Heaton had not actually been tested in the Clarets' goal and that was the case again three minutes into the second half when Mbokani wasted another decent heading opportunity.
But the best chances were starting to come Burnley's way as the visitors enjoyed their best spell since the opening stages, moving the ball well and getting in behind the Hull defence.
Barnes shot just wide from 25 yards after Brady and Andre Gray had opened up the hosts and Gray then sent an effort skidding just past the post after an excellenmt ball over the top from Wetswood had put the striker in the clear.
Both sides sensed the possibility of a potential winner and with an hour gone it was Hull's turn to rue a missed opportunity when Burnley were caught short at the back.
Bbokanui ferried the ball into the path of Grosicki but the Poland international wasted the chance with a first-time effort he curled wide of the far post.
It was nip-and-tuck but with just under 20 minutes to go Hull were handed a lead when Keane conceded a penalty as his raised arm made contact with the ball in a crowded penalty area following a Hull corner.
Michael Keane concedes the penalty...
Huddlestone just beat Heaton from the spot as the Clarets' skipper almost palmed his effort round the post.
But the Clarets were behind for just a matter of minutes as Keane swiftly made amends with a superbly taken equaliser.
Brady's deep corner by-passed everyone bar Keane, who coolly chested the ball down before burying a low volley past Jakupovic from just inside the six-yard box to claim a perfectly-timed second goal - and second away-day point - of the season.
... but makes immediate amends
Barnes, booked following the award of the penalty, picked up a second caution in injury time and will miss next Saturday's trip to Swansea but the Clarets will go into the second of four successive away games in upbeat mood after finally getting a fitting reward on their travels.
Burnley: Heaton, Lowton, Keane, Mee, Ward, Boyd, Barton, Westwood (Tarkowski 85), Brady (Arfield 89), Barnes, Gray (Vokes 85). Substitutes: Robinson, Flanagan, Agyei.
Booked: Westwood, Barnes.
Sent off: Barnes
Hull City: Jakupovic, Elabdellaoui (Hernandez 82), Robertson, Maguire, Ranocchia, Elmohamady, Huddlestone, N'Diaye, Maloney (Meyler 67), Grosicki, Mbokani (Niasse 67). Substitutes: Marshall, Hernandez, Diomande, Tymon, Bowen.
Referee: Martin Atkinson