Tommy Johnson scored Celtic's winner at Parkhead to keep their 100 per cent start to the new season intact. Johnson got the chance to impress with Chris Sutton suspended ahead of transfer-listed youngster Mark Burchill and he showed O'Neill that he too could play in his Parkhead revolution.
However, Swedish international striker Henrik Larsson can make most strikers stand out and he rescued his side with the second-half equaliser after Kilmarnock had threatened to end their unbeaten run when they took the lead through a glorious Andy McLaren strike.
Kilmarnock stunned the home crowd in the 18th minute to take a shock lead when McLaren curled a brilliant right-foot shot from 25 yards into the top corner.
However, Larsson got Celtic back on level terms in the 50th minute, drawing Gordon Marshall before sliding a right-footed passing shot past the keeper.
And it was the Swede who created the winner in the 73rd minute when he played the ball through to Johnson, who beat the offside trap, before casually slotting the ball into the corner.
However, Kilmarnock's misery increased in the very final minute when Martin Baker was dismissed for a foul on Moravcik and referee Kenny Clark had no hesitation in brandishing a second yellow card.
Celtic: Gould, Stubbs, Valgaeren, Boyd (Mjallby 46), Mahe, Lambert, Moravcik, Petrov, Petta, Larsson, Johnson. Subs Not Used: Kerr, Berkovic, Burchill, Tebily. Booked: Petrov, Petta, Stubbs, Lambert. Goals: Larsson 50, Johnson 72.
Kilmarnock: Marshall, MacPherson, Dindeleux, Hessey, Baker, Canero, Holt, Mahood (Cocard 85), Fowler (Vareille 40), McCoist (Wright 77), McLaren. Subs Not Used: Meldrum, Hay. Sent Off: Baker (89). Booked: McLaren, Baker. Goal: McLaren 17.
Referee: Kenny Clark (Scotland).