Paul Sturrock's side enjoyed long periods of possession but their manager's pre-match warning that Jason Koumas and Cameron Jerome would pose a major threat was proved accurate as the duo put the visitors in control.
Jerome was particularly impressive, scoring twice and hitting the woodwork twice in the first half, showing the form that has earned him a place in Peter Taylor's squad for England's Under-21 European championship play-off match against France tomorrow evening.
"He was awesome in the first half," Jones said of the 19-year-old, who has already been linked with moves to Tottenham, Charlton or Chelsea in January, before stressing that he believes the young striker's interests would be best served by remaining with Cardiff.
"He is a talent but he is nowhere near ready yet and a move to the Premiership at this stage could be his downfall. He can improve in many ways but he will only do that with the experience of playing competitive games against good defenders and he will not get that in a Premiership reserve side."
Cardiff's first-half blitz followed four games without a goal but it took only nine minutes last night for Koumas to end that run as the Welsh side scored their first goal in 385 minutes of play. The former West Bromwich Albion player, who has been outstanding in Cardiff's recent progress, turned finisher to head home Rhys Weston's cross.
Jerome had already seen a shot hit the bar and a diving header thud against the post before he rose to head home his ninth goal of the campaign from a Koumas cross in the 30th minute, before firing home his 10th eight minutes later as Jeff Whitley's pass caught the rearguard flatfooted.
Chris Eagles gave the home side a shred of hope with a neatly taken goal after 64 minutes but an improved performance in the second half was of scant consolation to Sturrock. "We were casual and sloppy in the first half and paid dearly for it," he said.
Sheffield Wednesday (4-4-2): Weaver; Simek, Lee, Wood, Heckingbottom; Eagles (Partridge, 80), O'Brien, Whelan, Brunt; Graham (Agbonlahor, 80), Corr (Bullen, 61). Substitutes not used: Adamson, Rocastle.
Cardiff City (4-4-2): Alexander; Weston, Purse, Loovens, Barker; Cooper (Parry, 59), Whitley, Ledley, Koumas; Lee (Ardley, 88), Jerome. Substitutes not used: Cox, Margetson (gk), Ricketts.
Referee: T Kettle (Berkshire).Reuse content