Both previous games this season have been won 1-0 by the away team, with Killie six points and two places above the Tynecastle side.
Leaders Celtic beat St Johnstone in midweek to go six points clear at the top and face Saints at McDiarmid Park on Sunday, live on Sky Sports at 12.30pm. There are four games on Saturday - Hibernian and Aberdeen meet at Easter Road where the teams have drawn twice in normal time this season, with the Dons winning on penalties in the Betfred Cup.
Second-placed Rangers are at home to St Mirren, who they have twice beaten 2-0 this season. New Hamilton Accies head coach Brian Rice takes charge for the first time against fellow strugglers Dundee at the Hope CBD Stadium while Motherwell are aiming for a fourth straight league win when they play Livingston at Fir Park.
Ladbrokes Championship leaders Ross County have a three-point lead at the summit as they prepare to face Dunfermline Athletic at East End Park while second-placed Ayr United play Alloa Athletic at the Indodrill Stadium.
Dundee United, who have been one of the busiest clubs in the transfer window, welcome Morton to Tannadice and fourth-placed Inverness CT are at home to a Partick Thistle side who are yet to win away. Falkirk, still seeking their first home victory of the campaign, face Queen of the South at the Falkirk Stadium.
There are three matches in Ladbrokes League 1, including second-placed Raith Rovers against in-form Forfar Athletic at Stark's Park. Airdrieonians, in fifth spot, welcome second-bottom Dumbarton to the Excelsior Stadium and there's a local derby at Links Park where Montrose play Brechin City. Stranraer v Stenhousemuir at Stair Park has been postponed and rearranged for this Tuesday, February 5, at 7.45pm.
Four games have been postponed in Ladbrokes League 2 so leaders Edinburgh City can go four points clear when they play bottom club Albion Rovers at Ainslie Park.
Meanwhile, East Fife are in Dublin to take on Bohemians in the quarter-final of the IRN-BRU Cup on Saturday, with the winners away to Ross County in the last four.