A 3-0 victory over Hibernian keeps the Jags above Neil Lennon's side on goal difference, while Motherwell won again and Hearts drew 0-0 with Dundee United
The table-toppers suffered a 1-0 loss to Aberdeen in their previous league match, but they were back on form at the Tulloch Caledonian Stadium as Billy Mckay scored twice to take his goal tally to eight for the season, either side of an effort from Richie Foran.
That gave Inverness top spot from Celtic on goal difference, although Neil Lennon's men continued their push with an impressive 5-2 victory over Kilmarnock.
The visitors maintained their unbeaten start to the new campaign at Rugby Park courtesy of a hat-trick from Georgios Samaras.
The 28-year-old’s first two efforts capped off three goals in just 10 minutes for Celtic, after Kris Commons had put them ahead on the 20-minute mark.
Goals late in the first half from Sammy Clingan and Sean Clohessy gave Kilmarnock brief hope of a comeback, but Samaras and Amido Balde struck late on to seal the victory.
Elsewhere, Motherwell continued their good start with a 3-1 win over Ross County, with striker John Sutton netting twice, while the points were shared in Saturday’s other two fixtures.
Neither side was able to clinch a winner as St Johnstone hosted Partick Thistle, with Steve MacLean cancelling out Kris Doolan’s sixth-minute effort in a 1-1 draw, while Hearts were also held 0-0 by Dundee United.