Despite positive signs under new manager Neil McCann, Kilmarnock remain three points behind third bottom St Mirren.
Perhaps inspired by their 4-3 midweek win over St Mirren, McCann’s side took the initiative from kick-off.
At the other end, Daizen Maeda stung the palms of home goalkeeper Kelle Roos with a powerful drive, but Kilmarnock were quickly up the other end to score on the break.
Just when John-Jules appeared to make a mess of his charge into the penalty box, he slipped inside Auston Trusty and curled his drive into the far corner.
Having added to his midweek hat-trick, the big striker turned provider as his chip into the six-yard box was met by Hugill, whose header looped over scrambling goalkeeper Kasper Schmeichel.
Kilmarnock survived some late first-half pressure, but the introduction of new signing Alex Oxlade-Chamberlain, Tomas Cvancara and Tounekti at the break turned the game.
Tounekti had already threatened before he cut inside and found the far corner with a trademark finish.
Celtic were back level when Kilmarnock failed to clear a long throw and Nygren stabbed in his 13th league goal of the season.
John-Jules fired a free-kick against the crossbar as both sides chased a winner.
However, it was Celtic who were creating the better chances and their pressure told when a tiring Kilmarnock failed to clear inside their penalty box and on-loan Bournemouth right-back Araujo swept in his first goal for the visitors to ignite wild scenes among the visiting fans.
