Livi travelled north without injured duo Goran Stanic and James McPake, while Craig Brewster missed out for Caley Jags due to a knee injury.
Barry Wilson was first to come close when his free-kick had to be clutched by Roddy McKenzie then he flashed another just wide moments later from a similar range.
Ian Black and Russell Duncan then combined to set up skipper Stuart Golabek who cracked a low drive wide.
Black then came to the rescue when he headed off the line a Derek Lilley header which he connected with from a Burton O'Brien corner.
Bryan Prunty missed from just eight yards after Graham Bayne put him through on 26 minutes.
It was Livi though who grabbed the lead when O'Brien's corner was headed into the net from eight yards by Dair. The defence were too slow to get to him.
The task in hand got tougher when Wilson was forced off after a knock, although the bustling Richie Hart replaced him.
A series of chances from Inverness failed to produce a goal and the Lions led at the half-time break.
Lilley was denied just into the second half by a great save from Mark Brown when he pushed his shot on to the bar.
Then Hart's free-kick was well dealt with by keeper McKenzie. On 65 minutes a decent Black shot was also held.
Hart then tested McKenzie with a free-kick, but the keeper got down well.
He saved from Bayne on 71 minutes after Tokely, Hart and sub Rory McAllister combined.
Livi keeper McKenzie saved another two decent chances before the end, while poor Inverness finishing proved costly.