Hibs have already seen arch rivals Hearts relegated into the second tier and their latest defeat means they could follow them into a division that will also contain Scottish giants Rangers next term.
Terry Butcher's men could have secured their survival with a final-day win over Kilmarnock, but it was the visitors who avoided relegation themselves.
Kris Boyd scored the game's only goal in the 44th minute, as Hibs – who hit the bar and had an effort cleared off the line – saw their winless stretch to 13 matches.
Jordon Forster went close in the early stages for Hibs before Scott Robertson's header was nodded off the line by Barry Nicholson.
Their early pressure amounted to nothing, though, and Boyd swept home from just inside the penalty area on the stroke of half-time.
Hibernian captain Liam Craig saw his 20-yard effort hit the underside of the bar in an attempt that summed up his side's day, and they were unable to convert any of their late chances as they finished the season with 35 points from their 38 matches.
Kilmarnock's win took them to 39 points and ninth position.
Hibernian will play the winner of the Scottish Premiership's play-off semi-final over two legs later this month, with the prize being a spot in the division next season.
Partick Thistle finished just three points above Hibernian after a 3-2 home defeat to Ross County.
The visitors claimed a 2-0 lead through goals from Jordan Slew and Yoann Arquin but Lyle Taylor and George Moncur responded for Partick to level proceedings.
Ross County substitute Melvin de Leeuw bagged the winner with 13 minutes left, though, as his side finished on top of the relegation group.
And Hearts' 31-year-stay in the top flight of Scottish football ended with a 1-1 draw at St. Mirren.
Conor Newton's first-half strike was cancelled out by Hearts forward Dale Carrick three minutes after the break.
Hearts – who were deducted 15 points in June for entering administration - finished the season 12 points adrift of Hibs, despite a run that saw them win five of their last seven matches.
