The Welsh club's chairman Mehmet Dalman had revealed prior to the game that Slade was "under scrutiny" after City had slipped away from the play-off race - and the win was also a well-timed boost for a side who had been hit by a transfer embargo on Friday.
Noone opened the scoring in the 28th minute and then doubled Cardiff's advantage eight minutes later.
Wolves forward Michal Zyro, who had scored twice on his home debut in Tuesday's 3-2 win against Fulham, did give Kenny Jackett's side hope when he reduced the arrears five minutes before half-time.
But Joe Ralls set the seal on Cardiff's success in the 48th minute as City secured their second win in six games - and ended Wolves' run of four successive Championship victories.
Wolves, watched by owner Steve Morgan for the first time since he put the club up for sale last September, tested the Cardiff defence in the opening stages with Conor Coady heading wide before Jordan Graham saw his rising drive fly over the bar.
Rajiv Van La Parra then wasted an excellent chance to break the deadlock in the 14th minute after he dispossessed Bruno Ecuele Manga, only to drag his range shot into the side-netting.
Having weathered the early storm, Cardiff were able to get a foothold in the game with Ralls seeing his powerful drive deflected wide after 16 minutes.
Stuart O'Keefe came even closer to giving the visitors the lead two minutes later - teed up after good work by Joe Mason, his curling 20-yard shot crashed to safety off the bar.
Wolves should have heeded that warning. There appeared to be little danger when Noone collected the ball 30 yards from goal - but, with Wolves not closing him down, he tried his luck and his shot dipped over Carl Ikeme and into the net.
Wolves rallied briefly after the shock of falling behind with Van La Parra firing inches wide, before Noone stunned them again with an even better piece of finishing.
This time, the 28-year-old was on the left hand edge of the Wolves area and he beat Ikeme with a curling left foot drive.
The hosts' uphill task looked even harder but they were inadvertently gifted a route back into the game by David Marshall.
The Cardiff goalkeeper could only palm out Van La Parra's low drive and Zyro was on hand to make no mistake from six yards and reduce the deficit to 2-1.
That should have given Wolves some impetus to take into the second half but it was Cardiff who made a flying start immediately after the interval - restoring their two-goal lead in decisive fashion.
Once again Noone was to the fore, this time racing to the edge of the Wolves area and rolling the ball into the path of Ralls, who calmly placed his low shot into the corner of the net.
Noone was outstanding but put a blot on his afternoon's work when he was booked for diving five minutes from time.
Wolves (4-4-2): Ikeme; Iorfa, Batth (c), Ebanks-Landell, Doherty; Coady (Henry, 45), McDonald, Edwards, Graham (Enobakhare, 65); Van La Parra, Zyro.
Subs: Martinez, Golbourne, Saville, Price, Byrne.
Goal: Zyro (40)
Cardiff (4-5-1): Marshall (c); Peltier, Manga, Connolly, Malone; Noone, O'Keefe, Whittingham (Fabio, 86), Ralls, Pilkington; Mason (Dikcagoi, 75).
Subs: Moore, Kennedy, Ameobi, Revell, Macheda.
Goals: Noone (28, 36), Ralls (48)
Referee: Dean Whitestone (Northamptonshire)
Attendance: 24,238 (1,057 Cardiff fans)