An early goal from George Oakley was enough as Scott Harrison's disallowed goal in the second half proved pivotal.
The Bairns came out of the traps relatively quickly and Tom Owen-Evans was close to finding Deimantas Petravicius in the box inside a minute, but the Lithuanian just failed to get contact on the ball under pressure.
Paul Hartley's side fell behind on 10 minutes, though, through George Oakley. A low ball into the box from Tom Walsh was knocked past Leo Fasan by Oakley from close range.
Returning striker Nathan Austin had a chance on 16 minutes but his header was blocked and easily gathered by Fasan.
The remainder of the first period was quiet, with Polworth smashing over for the visitors and Mark Ridgers in the away goals having next to nothing to do.
Into the second period and Falkirk picked up their game, Andy Irving looked lively and his cross was cleared by Tom Walsh.
On 54 minutes, the biggest chance of the second half for the visitors. Scott Harrison's header caused problems for Tom Dallison who slipped and allowed Nathan Austin in, but he was superbly denied by Fasan.
Falkirk thought they were level just a few minutes later. A perfect delivery was nodded home Scott Harrison, in off the post, but the goal was disallowed - seemingly for a push before Harrison got a head on the ball.
The Bairns had a couple of half chance thereafter as they searched for the all elusive equaliser.
Irving's shot was blocked and a corner into the box caused problems, with Dallison and Harrison's height causing the Inverness defence issues.
It was Caley Thistle who had the better chances in the closing stages, though. Right-back Shaun Rooney headed a corner narrowly wide before Liam Polworth curled an effort wide in stoppage time after a quick break.
Falkirk's league season, then, off to a slow start, with a trip to Partick Thistle next up.