On the park, they have struggled, falling eight points adrift of Hearts after being humbled at Tynecastle on Sunday. A bounce was badly needed against a Falkirk side who came into this off the back of two wins.
O’Neill reverted to experience, with three changes in defence and James Forrest deployed down the right flank.
A familiar pattern emerged, with Celtic showing intent, but they struggled to trouble goalkeeper Scott Bain at first.
The breakthrough came via the, at times wasteful, Nygren. He saw his strike bounce of a post with Kenny alert to fire in the rebound.
Falkirk came close to an immediate leveller when Trey Samuel-Ogunsuyi was denied by Kasper Schmeichel but, from there, Celtic took a firm grip.
Kenny seized on Nygren’s knock down to net his double, then Nygren capitalised on Bain’s poor parry and Tounekti seized on his chance to finish from close range.
It could have been more as Celtic enjoyed welcome relief from everything that has engulfed the club ahead of a crucial cup semi-final against Rangers.
