Celtic must have expected a prickly SPL fixture against Caley Thistle, having twice only edged past them 2-1 last season and drawing in Inverness last December.
These clashes always offer mouth-watering physical tussles all over the park, and power rather than skill are usually the order of the day.
The home team had to do without forward Barry Wilson through illness, with Liam Keogh making his 100th appearance for the club, against his former employers.
Inverness manager Charlie Christie opted to stick with striker Dennis Wyness in attack alongside Craig Dargo, despite the former Hearts ace not netting since February.
For Celtic, Stilian Petrov dropped out of the pool, with Stephen Pearson taking his midfield slot. Skipper Neil Lennon was back in the starting line-up with Maciej Zurawski dropping to the bench.
The champions needed the win to overtake rivals Rangers at the top of the table, while the Highlanders were seeking their first league win of the season.
The hosts were not overawed in the opening exchanges and the champions' defence were quick to close down Dargo when he looked to be in a threatening position at the edge of the area.
Bhoys gaffer Gordon Strachan, sitting in the stand as a result of his suspension from the sidelines he earned against Hearts recently, was soon watching his men settle into the game.
There was a fine save from Inverness keeper Mark Brown when he did well to deal with a decent on target drive from Jiri Jarosik, which could have stolen in at the near post.
They did take the lead though on 26 minutes when Kenny Miller was freed wide on the right and his delivery was knocked low past Brown by Pearson.
Christie's men reacted by winning a corner within a minute, but they were unable to capitalise on it.
Then Celtic took control again, searching for a second before the interval.
It was Caley Thistle though who almost levelled, a rasping John Rankin effort needing to be tipped over by Artur Boruc.
He then followed that with a wonderful swerving 25-yarder which flew past Boruc's left post.
Keeper Boruc had to be replaced at the start of the second half by David Marshall after picking up a knock.
Scotland striker Kenny Miller had a decent chance to extend the lead when he got the better of Ross Tokely but his shot was held by Brown on 58 minutes.
At the other end, just before he was replaced for Graham Bayne, Wyness saw his dipping shot drop just over the crossbar.
And Bayne tested Marshall within seconds when his shot was well saved.
With 13 minutes to go, Brown got down smartly to deal with a fine drive from sub Zurawski.
Then Caley Thistle, from nothing, drew level in sensational style when Munro smashed home a drive from the edge of the box.
There followed ten minutes of both teams going for the winner.
Miller just poked the ball past the post from the edge of the six-yard box when a cross came in from Shunsuke Nakamura.
A Pearson piledriver almost snatched a stoppage-time winner for Celtic, but Inverness held on for a deserved and valuable point.