After a relatively quiet opening period, it was Hibs who first threatened as Filipe Morais turned Richard Hastings inside out before fizzing the ball across the face of goal, but neither Clayton Donaldson or Steven Fletcher were able to apply the finishing touch.
Clear-cut chances were few and far between, but in a 60-second spell just before the half-hour mark both sides spurned opportunities to take the lead.
Hibs were first to go close as top-scorer Fletcher found himself one on one with Michael Fraser only to his effort blocked by the Caley Thistle goalkeeper.
Play then switched to the other end of the field and Yves Makaba-Makalamby had to look lively to turn away John Rankin's shot from 30 yards.
He may have been ploughing a lone furrow upfront, but Niculae was giving the Hibs rearguard plenty of problems and, after forcing Makaba-Makalamby into a comfortable save from close range, the Romanian finally scored his first league goal for Caley Thistle after 42 minutes.
In easily the best move of the match, Roy McBain's header was flicked into the path of Niculae via Rankin and he showed just why he has played for the likes Dinamo Bucharest and Sporting Lisbon by calmly lobbing the stranded keeper from just outside the box.
Hibs offered more of a potent attacking threat at the beginning of the second half and, after Fraser had done superbly to keep out Brian Kerr's shot from eight yards, the visitors struck the underside of the crossbar through Donaldson less than a minute later.
Slowly, however, Caley Thistle regained control of proceedings and all but put the game beyond Hibs 12 minutes from time with Niculae on hand to score once again.
This time he fired home at the second attempt after his initial shot had been blocked by a defender.
Rankin then went close to putting a gloss on the final scoreline late on, before Niculae was inches away from completing what would have been a memorable hat-trick in injury-time.