Hull's battle to preserve their Coca-Cola Championship status received a major boost as they held on to secure a priceless victory at Cardiff while Yorkshire rivals Leeds were held at home to Ipswich which all but condemns Dennis Wise's side to the drop.
Having been let off the hook twice in the opening 45 minutes Hull regrouped and in the end were full value for the three points as veteran striker Dean Windass scored in the 52nd minute.
The visitors started strongly with Nicky Forster having a shot blocked by Cardiff defender Darren Purse inside the opening two minutes.
The early exchanges were disrupted by a series of free-kicks but it was Hull, desperate for victory to ease their relegation fears, who then survived two big scares.
The home side carved out their first opportunity after nine minutes with a fine cross from Peter Whittingham finding the unmarked Thompson but he failed to get any power on his header which enabled Hull goalkeeper Boaz Myhill to save comfortably.
And just a couple of minutes later Steven Thompson missed an even simpler chance when he got on the end of a cross from Joe Ledley but from just six yards his header again failed to seriously trouble Myhill.
Cardiff continued to threaten and the visitors were indebted to Myhill, who superbly parried Roger Johnson's 30-yard piledriver after 17 minutes.
The home side continued to pepper the Hull goal and they went close again when Whittingham sent a long-range volley just wide of the upright.
Hull were also guilty of spurning a good opportunity just before the half-hour mark with Windass mis-hitting his shot from just six yards after a cross from Stephen McPhee.
But he almost made amends eight minutes before the interval with a superb 20-yard shot which brought the best out of Cardiff goalkeeper David Forde, who tipped the ball over the crossbar.
Hull boss Phil Brown made a tactical switch at the break, taking off former Arsenal and England midfielder Ray Parlour and replacing him with Dean Marney, but it was Cardiff who had the first opportunity of the second half with Forster firing wide from just six yards.
But Brown had every reason to celebrate after 51 minutes as Windass, having just been booked for leaving the field of play without obtaining the referee's approval, fired home after Forster's initial shot had been parried.
Just three minutes later the impressive Whittingham sent a shot just over the crossbar as Cardiff looked for an immediate response.
Both teams opted for changes just after the hour with Hull bringing on Nicky Barmby for McPhee and Cardiff replacing Whittingham with Willo Flood.
But despite plenty of endeavour the home side could not find an equaliser as Hull finished the stronger.
Teams:
Cardiff Forde, Blake, Purse, Johnson, McNaughton (Gunter 80),Parry (Ramsey 90), McPhail, Ledley, Whittingham (Flood 64),Thompson, Feeney.
Subs Not Used: Alexander, Green.
Hull Myhill, Ricketts, Turner, Delaney, Dawson,Parlour (Marney 46), Ashbee, Peltier, Windass, Forster,McPhee (Barmby 63).
Subs Not Used: Duke, Parkin, Coles.
Booked: Windass, Dawson.
Goals: Windass 52.
Att: 12,421
Ref: K Friend (Leicestershire).