Marney had scored just one League goal since February, 2011 and in four years as a Hull player found the net only nine times.
But the midfielder has been a key part of the Clarets’ attacking game-plan in recent weeks and this time he was at the sharp end as his clinical finish five minutes before half time gave Sean Dyche’s men a first win in three games.
It was also Burnley's fourth successive win at Hull as the hoodoo continued for a City side which had won six of their previous eight games but couldn’t find a way to hit back and break through the Clarets' magnificent back line.
A third clean sheet under Dyche’s care was therefore another tangible sign of progress after a superb first-half performance – capped by Marney’s moment of magic – was enough to give the Clarets victory in a game for the first time since January when they haven’t needed talismanic frontman Charlie Austin to get on the scoresheet.
With the suspended Kieran Trippier missing his first League game since joining the Clarets at the start of last season, David Edgar took over at right-back on the ground where he scored his first two goals as a Burnley player 12 months ago.
Dean Marney celebrates his winning goal
The Clarets showed a further change at left-back with the fit-again Ben Mee restored to starting duty and Dyche also welcomed back Ross Wallace at the first opportunity following his one-match ban.
And Wallace was instrumental in an excellent first 45 minutes from the Clarets, who thoroughly deserved to lead against a Hull side which had won its last three home games.
With just five minutes gone Wallace tested goalkeeper David Stockdale on his Tigers’ debut and the on-loan Fulham man was far from convincing as he almost parried a long-range shot into the path of the waiting Austin.
Stockdale then grabbed a deflected Martin Paterson shot at the second attempt after Paterson had also curled an effort wide after intercepting a wayward pass from Hull midfielder Seyo Olofinjana.
And that was typical of the way Burnley never allowed City to dictate, keeping their discipline and making excellent use of the possession they earned.
Jason Shackell might have made more of a volleying chance following a corner and Wallace was then only inches away with another thundering drive from long range which Stockdale finger-tipped onto the crossbar at full stretch.
Hull countered with their best spell of the half but Burnley’s re-shaped defence protected Lee Grant superbly and then five minutes before the break the Clarets pounced to go 1-0 up.
Austin was always a willing target as the Clarets' attacking outlet and when he held the ball up and spread the ball wide to Wallace, the winger had Hull on the run.
Tower of strength Jason Shackell
He might have gone alone but after cutting in made the match-changing decision to play a little reverse pass into the path of Marney, whose low shot on the turn back across Stockdale was superbly executed to give the midfielder the goal he had craved.
Chris McCann then lashed a shot just wide as he burst forward from midfield and Hull manager Steve Bruce reacted to being second best at the break by making a double change as Robbie Brady and David Meyler came on in a switch to a 4-4-2 formation.
And within five minutes the Tigers were almost back in it as low cross from Robert Koren was deflected onto the inside of a post by Paterson as he helped out his defence following a corner.
Hull still hadn’t created much of their own but with an hour gone they had a real chance to level as Ahmed Elmohamady picked out Stephen Quinn with a cross which the winger headed over the bar from eight yards out.
Burnley were unable to regain the control they had enjoyed in the first half as City cranked up the pressure, wasting a chance on the break when they had men over following a Clarets’ corner and then seeing substitute Nick Proschwitz volley over with his first touch.
Ben Mee digs in for a result
And with 15 minutes to go Dyche called for for fresh legs as Danny Ings and Sam Vokes were sent on to try and help stem the flow.
The pair did their bit with Vokes almost getting on the end of a pull-back from Paterson after Edgar had crossed deep in a rare Burnley attack.
But the real focus was at the other end as Hull tried to salvage an unbeaten home record stretching back to September.
The Tigers threw everything at Burnley but the Clarets simply refused to buckle, defending for their lives, blocking every ball that came into the penalty area and giving everything to become the first team to complete a shut-out at the KC this season and secure a thoroughly deserved third away win of the season.
Well played pal!
Hull: Stockdale, Rosenior (Proschwitz 69), Chester, Koren, Simpson, Olofinjana, Faye, Aluko, Elmohamady, Bruce, Quinn. Subs: McKenna, Evans, McLean, Jakupovic.
Burnley: Grant, Edgar, Mee, Duff, Shackell, Stock (Vokes 75), Marney, McCann, Austin (Bartley 89), Paterson, Wallace (Ings 75). Subs: Bartley, Lafferty, Stanislas, O’Neill, Jensen.
Booked: Austin 45, McCann 72, Paterson 90+3, Marney 90+4
Referee: Gary Sutton