The success saw them replace Jersey in fifth spot and keep alive hopes of making the top-four.
Jimmy Lowes’ side – who visit relegated Rotherham Titans next Saturday – were particularly impressive given they lost fly-half Callum Irvine to an injury inside just five minutes yet still scored four tries.
Andy Forsyth got the first score running in off Stevie McColl’s pass, McColl adding the first of his conversions.
Jersey responded after stealing a Carnegie line-out in the 24th minute, Irishman Jerry Sexton getting the try which Brendan Ciope improved, but the home side went in ahead.
Hooker Mike Mayhew – in for Joe Buckle – benefitted after a series of drives close to the Jersey line in the 37th minute.
The visitors started the second period strongly but Lowes’ side, crucially, escaped when winger George Watkins broke clear to release the pressure.
Chris Elder and Forsyth advanced the break before the latter was brought down by a high tackle. A rolling maul from that penalty saw recalled prop Charlie Beech get over for their third try, McColl improving.
Jersey were kept at bay until scrum-half Keiran Hardy crossed in the 61st minute, Cope converting, but it did not leave Carnegie in problems.
Five minutes later, Tom Bullough offloaded brilliantly to Kiwi flanker Richard Mayhew, the captain surging over from 10m out. Carnegie saw lock Ben West stretchered off late on with jersey’s Jared Saunders snatching a late late losing bonus point.