Some onlookers may have thought facing Hartpury on the final day of the Championship campaign would be a simple task for Chris Stirling’s side given the visitors to Emerald Headingley finished second bottom.
However, Hartpury almost pulled off a shock victory having fought back to gain the lead heading into the final stages only for Elder to strike in the 75th minute after centre Luke Eves had been sin-binned.
The victory meant Carnegie – bottom at Christmas – secured sixth spot, a remarkable turnaround in what has been a troubled campaign off the field.
Stirling, of course, now moves on to Cornish Pirates with the club switching to a part-time operation in light of recent budget cuts and plenty of players were playing their last game in club colours.
Carnegie repelled plenty of Hartpury pressure in the first quarter and then scored themselves when Matt Smith, the lock who will join Doncaster Knights, crashed over in the 22nd minute.
Elder converted and did so again when Miles Thoroughgood scored his third try of the season.
Hartpury hooker Luke Stratford responded, Sam Leeming converting to leave the visitors 14-17 behind at the break.
Dan Temm scored at the start of the second period after Carnegie won the ball back at the kick-off, but then came the Hartpury rally as Tom Dodd and Toby Venner both crossed, Leeming converting each time for that surprise lead.
The visitors’ discipline fell away, though, to give Carnegie one last chance.