Dick Campbell's cinch Championship runners-up had the better of the opening half but Caley Thistle improved and Logan Chalmers came closest to breaking the deadlock in the first leg of the Premiership play-off semi-final.
Arbroath fans hailed their team after the final whistle and will be optimistic ahead of the second leg - their team's last home defeat in the league came last July, although it was against Caley Thistle.
Inverness came into the game on a high after winning eight of their last 10 matches, but Arbroath harried them into mistakes and created some decent early chances.
Jack Hamilton's header set up Michael McKenna but the attacker could not get over the top of the ball and fired over in mid-air.
Several Nicky Low set-pieces caused problems in the home defence and the former Aberdeen player forced a decent stop with a direct effort from a free-kick.
Inverness improved towards the end of the half and Chalmers hit the bar with a powerful 25-yard effort.
The on-loan Dundee United winger had an easier chance 20 minutes into the second half. Robbie Deas burst forward from central defence and played in Chalmers, who emerged from a challenge with the ball but steered a shot just beyond the far post.
Sean Welsh then sent a ball over the top to find Austin Samuels' run in the left channel but the forward's bouncing strike was pushed wide by Derek Gaston.
The home side kept pushing. Aaron Doran volleyed over from the edge of the box after getting on to a flick-on, while Kirk Broadfoot headed over from close range after beating Gaston to Reece McAlear's corner.
Arbroath settled following the flurry of chances and saw out the game.