At a time when the visitors sit 12 points clear at the top of the standings, the home side are just three points above bottom place.
Match preview
Although Celtic had won 22 of their 23 matches heading into last weekend, there was an acknowledgement that defeat to Rangers would re-open the title race.
However, coming through with a 3-2 victory over their Old Firm rivals has realistically ensured that Celtic will retain the title weeks before the end of the season.
The gap to Rangers now stands at 12 points at a time when Celtic have won 27 of 29 matches in the top flight this campaign, yet Ange Postecoglou will demand that Celtic maintain their relentlessly high standards.
While Celtic have kept just one clean sheet in their last five league outings, their three-goal haul at Parkhead last weekend has moved them to within two strikes of triple figures.
Reaching that milestone is a foregone conclusion, but Postecoglou will be motivated to set as many records as possible to cement a legacy at the club.
From Kilmarnock's perspective, they will simply settle for survival in the Scottish Premiership at a time when the battle to avoid the drop could become a three-horse race.
Tenth-placed Kilmarnock are now four points adrift of St Johnstone, while just three points separate them from bottom-of-the-table Dundee United, who won last weekend.
Nevertheless, Derek McInnes will feel encouraged that seven points have been accumulated from five matches, their defeats coming at Rangers and Aberdeen.
That said, when Celtic visited Rugby Park back in August, they left with a 5-0 win, and McInnes will no doubt take that into consideration on Sunday.
Kilmarnock Scottish Premiership form:
L
D
L
D
W
L
Kilmarnock form (all competitions):
D
L
L
D
W
L
Celtic Scottish Premiership form:
W
W
W
W
W
W
Celtic form (all competitions):
W
W
W
W
W
W
Team News
Postecoglou may be prepared to name the same Celtic XI from the win over Rangers.
Tomoki Iwata is an option to make just a second league start in midfield, but Aaron Mooy is more likely to get the nod.
While James McCarthy is ruled out through injury, the likes of Reo Hatate and Liel Abada both feature in the doubtful category.
With Rory McKenzie serving the second game of his ban for a red card versus Hearts, McInnes could settle for going with the same 3-5-1-1 setup which he opted for against Aberdeen.
Kyle Vassell is a doubt after missing out through injury last time out, while Innes Cameron and Ben Chrisene are also sidelined.
Kilmarnock possible starting lineup:
Walker; Mayo, Wright, Dorsett; Armstrong, Watson, Lyons, Donnelly, Chambers; Jones, Doidge
Celtic possible starting lineup:
Hart; Johnston, Carter-Vickers, Starfelt, Taylor; Mooy, McGregor, O'Riley; Jota, Furuhashi, Maeda
We say: Kilmarnock 0-3 Celtic
Although Kilmarnock have shown signs of improvement in recent weeks, it will surely not be enough to trouble their next opponents. Celtic know that the title is within their reach, and we expect another ruthless performance for the Glasgow giants this weekend.