Bellamy, back in the squad following a calf injury, stepped off the substitutes' bench in the 64th minute on Saturday and clipped home a 20-yard strike to break the deadlock three minutes later.
Whittingham coolly slotted home from the spot in the 73rd minute after Leeds defender Tom Lees had scythed down Cardiff striker Nicky Maynard and, although Jamaica international Rodoplh Austin fired home a 30-yard thunderbolt for Leeds with 13 minutes left, Malky Mackay's side held on to secure their third Championship win of the season.
Leeds have not beaten Cardiff since a 1-0 win at Ninian Park back in February 1984 and have now failed to get the better of their Welsh rivals in 14 meetings.
New loan signing Michael Tonge made his debut for Leeds in central midfield, but the visitors were dealt an early blow when striker Ross McCormack was forced out of the action in the fifth minute against his former club with what appeared to be an ankle injury, with Luke Varney replacing the Scotland international.
Varney's close-range effort was blocked by Cardiff defender Kevin McNaughton soon after and Leeds teenager Sam Byram, playing in midfield today, saw his header comfortably held by home goalkeeper David Marshall.
Neither side created a chance of note for the rest of a scrappy first half, which was punctuated by a series of full-blooded challenges, until Cardiff twice went close just before the break.
Striker Maynard's shot was blocked by Austin and another Cardiff summer signing, Heidar Helguson, headed Whittingham's corner over the crossbar.
Leeds boss Neil Warnock sent on striker El-Hadji Diouf for defender Adam Drury at the start of the second half, but Mutch and Whittingham threatened for the home side with long distance drives that flew wide.
Visiting goalkeeper Paddy Kenny then held Tommy Smith's 25-yard effort and caught defender Mark Hudson's close-range header as Cardiff chased the game's opening goal.
Bellamy replaced winger Noone in the 64th minute and three minutes later the former Manchester City livewire broke the deadlock.
Tonge was booked for his nasty challenge on Maynard 20 yards from goal and Bellamy curled the subsequent free-kick beyond Kenny and into top corner.
Cardiff doubled their advantage six minutes later. England under-21 defender Lees cut down Maynard in the area and referee Paul Tierney did not hesitate in pointing to the spot, with Whittingham coolly side-footing the resulting penalty into the bottom corner.
But Leeds hauled themselves back into the game when Austin blasted home a low free-kick from 30 yards following Aron Gunnarsson's foul on Varney.
Leeds defender Lee Peltier almost snatched a point for the visitors in the 87th minute, but headed over the crossbar and Cardiff held on for all three points.