Cameron Jerome's first-half strike kept Cardiff in the play-off hunt and condemned injury-hit Sheffield Wednesday to a fourth straight Coca-Cola Championship defeat.
The 19-year-old striker swept home Jason Koumas' near-post corner in the 19th minute, but Bluebirds goalkeeper Neil Alexander denied Wednesday on numerous occasions as Paul Sturrock's relegation-threatened outfit went down fighting at Ninian Park.
The visitors dominated the closing stages and were unlucky not to salvage a draw, with Jerome's 18th goal of the season proving decisive.
Cardiff boss Dave Jones made no changes to the side that began against Watford last week, while Paul Sturrock recalled Deon Burton and on-loan Yoann Folly to Wednesday's starting line-up in place of Steve MacLean and Richie Partridge respectively.
Visiting goalkeeper Chris Adamson was pressed into early action, holding on to Steven Thompson's close-range header from Koumas' cross and then getting down to parry Darren Purse's shot.
Riccardo Scimeca then headed Koumas' corner over the crossbar before Wednesday responded with Burton latching on to Tudgay's cross at the other end, only to steer the ball wide.
But the early promptings of Koumas paid dividends for Cardiff as Jerome stole in at the near post from another corner to rifle the ball beyond Adamson, low into the centre of goal.
Jeff Whitley tried his luck with a right-footed shot from the edge of the penalty area that flew wide as Cardiff looked to double their advantage.
Wednesday midfielder Chris Brunt was off target when he let fly from 20 yards and Sturrock's side fought doggedly on the back foot, but Jerome threatened again for the Welshmen when he headed Neal Ardley's cross just over the crossbar.
Tudgay almost got the Owls back on terms in spectacular fashion, but Alexander was equal to his overhead kick and then a left-foot shot just before the break.
Wednesday went close to levelling again not long after the restart when Burton fired over from close range following Tudgay's cross, while Glenn Whelan's shot fizzed over as Sturrock's side resumed in determined fashion.
Republic of Ireland Under-21 international Whelan came to the fore in midfield for the visitors, who tested Alexander again when Bullen fired goalwards following Brunt's corner.
The latter was withdrawn by Sturrock and replaced by on-loan striker Leon Best as Wednesday looked to rescue a crucial point.
Whelan again worked an opening on the edge of the penalty area before unleashing a goalbound shot that Alexander punched clear and Burton headed wide when well placed from O'Brien's cross.
Wednesday dominated the closing stages. Tudgay shot over from 12 yards following another corner, but Cardiff held firm and Jerome flashed a 25-yard shot wide late on following a swift counter-attack.
Best's header from Whelan's cross was brilliantly saved by Neil Alexander, who then caught Graham Coughlan's effort as the Owls threw caution to the wind.
Teams:
Cardiff Alexander, Ardley, Purse, Cox, Barker, Koumas,Whitley, Scimeca, Ledley, Thompson (Ndumbu-Nsungu 90), Jerome.
Subs Not Used: Margetson, Weston, Loovens, Ferretti.
Goals: Jerome 19.
Sheff Wed Adamson, Bullen, Coughlan, Collins, Simek,Brunt (Best 77), Whelan, Folly, O'Brien, Tudgay, Burton.
Subs Not Used: Kirby, Partridge, Spurr, Rocastle.
Att: 11,851
Ref: L Probert (Gloucestershire).