Rangers still hold a 10-point lead over their great rivals, an indication that there is much work to be done by Celtic.
The early signs were encouraging for Celtic, with Lubomir Moravcik finishing off a three-man move with a volley that missed the target by inches. That proved a false dawn with the home side disjointed in their passing movements while the Kilmarnock midfield, hunting in packs kept possession effectively. As usual Ian Durrant, the former Rangers player, was keen to demonstrate his skills to the Celtic support and he was ably backed up by Gary Holt.
Holt found space 20 yards from goal to send in a shot in the 20th minute but his effort travelled along the ground. Kilmarnock were giving every indication at that stage of the tidy keen pattern that had taken them to second place.
Only towards the end of the half was there excitement as both sides came close to scoring. Regi Blinker saw his 37th-minute shot pushed wide by Gordon Marshall and a minute later Durrant freed Alex Burke, who beat the off-side trap but though his shot was wide of the goalkeeper, the ball hit the post and bounced to safety.
Celtic manufactured the breakthrough early in the second-half. A corner was swept high into the heart of the goalmouth where Riseth rose to head the ball past Marshall.
Celtic were unable to capitalise quickly on their advantage as Kilmarnock continued to hold the possession in the midfield area although rarely were they able to exert real pressure. Harald Brattbakk almost found a way through when he picked up a Blinker pass but he was crowded out.
In the 70th minute Tosh McKinlay came close to adding to Celtic's lead when his shot bounced wide off a post.
Kilmarnock suffered a blow in the final minute when Gus MacPherson was carried off on a stretcher.
Celtic (3-4-1-2): Gould; Mjallby, Riseth, Mahe; McNamara, Lambert, Blinker, McKinlay; Moravcik; Larsson; Brattbakk. Substitutes not used: Burley, Jackson, Healy, Burchill, Kerr (gk).
Kilmarnock (4-4-2): Marshall; MacPherson, Montgomerie, McGowne, Baker; Mahood (Roberts, 88), Holt, Durrant, Burke (Henry, 74); McCoist (Wright, 70), Reilly. Substitutes not used: Lauchlan, Strain (gk).
Referee: J McCluskey (Stewarton).