Bellamy struck his ninth goal of the season midway through the first half and substitute Emmanuel-Thomas headed home a knockout blow halfway through the second.
The Welsh side, chasing a return to the top flight for the first time since 1962, leapfrogged Norwich into second place after an impressive away display that carried all the cut and thrust that the Blades are desperately lacking.
The Yorkshire side, last in the third tier of English football in 1983, have now won only twice since manager Micky Adams was installed on a rescue mission following Gary Speed's departure in late December.
The Blades, undone by an 89th-minute winner in a 2-1 home defeat to Middlesbrough on Saturday, were unchanged, while goalkeeper Stephen Bywater and left-back Lee Naylor were recalled to Cardiff's starting line-up.
Bluebirds captain Craig Bellamy fired in the first shot on target in the 11th minute, forcing Blades goalkeeper Steve Simonsen into a low save.
But Simonsen was helpless to prevent the Welshmen taking a 21st-minute lead.
Peter Whittingham played Bellamy into the edge of the penalty area and the striker cut inside to fire an angled drive that deflected off Blades defender Neill Collins and inside Simonsen's left-hand post.
Simonsen flung himself full-length to palm away another rising shot from the busy Bellamy six minutes later and while the home side were often neat in their approach play, they carried none of the threat provided by the visitors at the other end.
Referee Mike Oliver was unimpressed by Jay Bothroyd's appeals after he was sent tumbling in the box by Collins, but his link-up play with Bellamy just before the break almost delivered a second goal.
Bothroyd galloped unopposed deep into Blades territory and clipped an inch-perfect cross which Bellamy volleyed first-time inches wide.
Blades defender Harry Maguire made his debut as a 48th-minute substitute for Joe Mattock, with Nick Montgomery having replaced Nyron Nosworthy at half-time.
Darcy Blake and Emmanuel-Thomas were sent on for Cardiff pair Naylor and Stephen McPhail respectively.
Matthew Lowton's header from Bjorn Helge Riise's corner, albeit straight at Bywater, gave the Blades faithful heart early in the second half, while a superb recovery tackle from Kevin McNaughton denied Blades skipper Darius Henderson.
Lowton rifled a shot over the crossbar as the Blades rallied and McNaughton's intervention again soon after denied Riise getting his shot away inside the area.
Henderson just failed to reach Lowton's fine curling cross, but a swift counterattack from the visitors resulted in their second goal.
Chris Burke provided the pinpoint cross and Emmanuel-Thomas rose highest to head home from a central position six yards out.
The home side refused to throw in the towel. Adams sent on forward Marcus Bent for Henderson, but his introduction made little difference to a hard-running side lacking guile and conviction.