Caley Thistle are now three points clear, with St Johnstone a point ahead of the defending champions, following Saints' 4-0 defeat of Ross County.
Richie Foran's early header and Billy McKay's third goal in as many games nine minutes from the interval moved Caley Thistle two points clear.
Inverness were looking to maintain their perfect start to the new campaign and it took them only four minutes to get off and running.
Graeme Shinnie's free-kick towards the far post found Foran throwing his head towards the ball and sending a lovely effort from eight yards beyond exposed Motherwell goalkeeper Lee Hollis.
Doran was having an outstanding game and it was his incisive pass that was chased down behind the Well rearguard by David Raven, who found McKay to convert from close range in the 36th minute.
Two goals in either half ensured St Johnstone cruised to victory over hapless Ross County, who remain pointless after their first three games.
Last season, the Highlanders pushed St Johnstone all the way for third place and a Europa League spot, but there was a clear gulf in class between the two sides today, with Nigel Hasselbaink and David Wotherspoon putting the Perth side two goals to the good after 18 minutes.
Wotherspoon would miss from the spot shortly before half-time, but it mattered little as Stevie May and Dave Mackay netted after the interval to seal a comprehensive win.
A Kris Commons penalty had set Celtic on their way as Jamie Langfield's red card sparked the end of Aberdeen's perfect start to the season.
Commons converted on the stroke of half-time after the goalkeeper had been shown a straight red card for bringing down Georgios Samaras.
The incident turned a finely-poised contest in Celtic's favour although they had to wait until the 87th minute to put the game beyond the 10 men when James Forrest broke clear to net.
Scott Robertson's late equaliser relieved the pressure on under-fire Hibernian boss Pat Fenlon as the Edinburgh club ended a run of four-straight defeats to draw with Dundee United.
Stuart Armstrong had put the Tannadice men ahead after 29 minutes as it appeared Fenlon's 18-month spell as manager was in real jeopardy before Hibs levelled with nine minutes left.
Robertson first tried to hit one from 25 yards out but saw it blocked by a United leg. The former Scotland midfielder remained alert, however, and smashed the rebound into the bottom corner.
St Mirren claimed their first point of the season with a 1-1 draw against Kilmarnock at St Mirren Park.
Gary Harkins' first goal for St Mirren against his former club cancelled out Kris Boyd's opener to give Danny Lennon's men a point.
But it could have been all three after a foolish punch from Boyd reduced Kilmarnock to 10 men for the final half hour giving the initiative to the home side.