The winger had missed a simple conversion attempt after Harry Davey's try to leave his bottom-placed side still trailing Doncaster Knights 22-20 in the 65th minute.
However, having earlier switched to full-back, he quickly dusted himself down to score a superb 40m solo try just three minutes later to glean the win but also a bonus point.
Elder left a raft of defenders in his wake and then converted to give his side only their second league victory of the season and certainly a much-needed one.
Carnegie had lost eight of their opening nine league games but - with a plethora of new signings - regained confidence with five wins from six in the Championship Cup to enter this crucial contest in high spirits.
It was a close contest, though, as expected against a Doncaster side who were desperate to end a four-game losing run and were strengthened by the return of Tonga fly-half Kurt Morath and hard-running flanker Ollie Stedman.
After Elder slotted a penalty, Knights were pushing hard at the end to salvage something and looked set to do so.
But after Carnegie's Tom Hill's professional foul, an eight minute wait for the TMO ruled the penalty should be reversed following Josh Tyrell's late clean-out.
Both players were sin-binned but Doncaster's chance had gone and Carnegie got the win that lifted them off the foot of the table.
There had been no score in the opening quarter until Knights - with their first attack of note - went over via a driving line-out, Rory Pitman scoring with Morath improving the 19th minute score.
It had come after they had forced a penalty on Carnegie's own scrum 20m out but the visitors responded immediately following a superb break and flick pass from Pete Lucock, Dan Temm proving the benefactor.
Chris Stirling's side then hit them with a quick double-strike, following a splendid line-out set move in the 25th minute.
Openside Josh Bainbridge wheeled infield from the back but it was a dummy run and, instead, scrum-half JB Bruzulier popped up to run straight through the middle untouched as Doncaster defenders were left bemused.
Chris Elder converted for a 12-7 lead only for Stedman to level things up on the half-hour with another slick try following some sustained pressure.
Elder's penalty just before the break saw his side regain the lead but, systematic of what had been a frustrating half for both teams, Doncaster then missed touch with a kick for the corner in the last play.
Nevertheless, Clive Griffiths' side came out for the second period re-energised with wingers Curtis Wilson and Paul Jarvis both finding space down their respective flanks and Tyrell making another midfield bust.
It was no surprise when they took the lead on 50 minutes, from a clever line-out of their own, Pitman - who excelled all afternoon - switching it blind for Tom James to supply Henry Seniloli, the scrum-half who had just come on as an emergency winger in place of Jarvis.
Morath slotted from wide out to put his side 22-15 up but he was injured soon after and then came that Carnegie turnaround in front of a crowd of 2,006.
Doncaster Knights: Cowell; Wilson, Creed, Owen, Jarvis (Seniloli 48); Morath (Olver 70), James; Hislop (Williams 70), Hunter (M Mayhew 61), Quigley (Sproston 70), Challinor (Ryan 80), Tyrell, Stedman, Hills, Pitman (Ryan 68).
Yorkshire Carnegie: Thoroughgood (Davey 47); Elder, Forsyth, Watkins; Te Rure, Bruzulier; Thomas, Buckle (Donnellan 76), Foster (Mitchell 56), Lemalu (Wilson 55), Smith, Romaine (R Mayhew 49), Bainbridge, Temm.
Referee: Michael Hudson