Dundee United escaped from Caledonian Stadium with a point to ease the pressure on manager Gordon Chisholm.
Lee Miller gave the visitors the lead from the penalty spot after being brought down himself by Grant Munro.
Ross Tokely equalised soon after with an acrobatic overhead kick, following which Inverness Caledonian Thistle took control of the game.
But United came close to snatching victory when Mark Brown superbly turned a Miller header on to the crossbar.
United had been without suspended Paul Ritchie, with Stuart Duff replacing the captain in defence.
But the away side took the lead with their first meaningful attack in the seventh minute.
Miller was set to pull the trigger when Grant Munro intervened with a sliding tackle, taking the striker's legs from under him.
Referee Calum Murray awarded a penalty to the visitors and Miller fired the spot-kick low to the right-hand side of Brown.
Inverness, unchanged after a fine run, were level when David Proctor swung a corner to the edge of the box, which midfielder Ian Black headed back into the area towards Ross Tokely.
The defender confidently cushioned the ball on his chest before acrobatically executing a delightful overhead kick past Derek Stillie in the United goal.
Caley Thistle were forced into a reshuffle in the 35th minute when Alan Morgan replaced the injured Proctor.
Black fired Wilson's delivery over the bar and Craig Dargo sent a shot on the turn from 18 yards out straight into the chest of Derek Stillie.
The United goalkeeper then watched Morgan blast a volley from an acute angle across the face of his goal.
Dargo fired another effort from distance straight into the arms of Stillie.
United rarely threatened after the break but were denied a second goal when Miller saw his powerful header tipped on to the bar via an outstanding save from Brown.
After the ball rebounded off the frame of the goal, Jim McIntyre was the quickest to react.
But, under pressure from Darren Dods and Tokely, his wild effort flew over the bar.
David McCracken then headed wide from a Robson free-kick.
Inverness came closest to scoring a winner when Wilson's 88th-minute free-kick was well saved by Derek Stillie, but this evenly-contested match was always destined to end in a draw.
Inverness CT: Brown, Tokely, Dods, Munro, Hastings, Proctor (Morgan 35), Black, Duncan, Wilson (Hart 88), Bayne, Dargo (Juanjo 83).
Subs Not Used: Fraser, Wyness, Fox, Brewster.
Booked: Dods, Morgan.
Goal: Tokely 20.
Dundee Utd: Stillie, Wilson, McCracken, Archibald, Duff, Samuel, Kerr, Fernandez, Robson, Miller, McIntyre.
Subs Not Used: Samson, McInnes, Dodds, Kenneth, Robertson, Cameron, Goodwillie.
Booked: Robson.
Goal: Miller 7 pen.
Att: 3,239
Ref: C Murray