There was little in the way of quality football on a heavy pitch and the Inverness side did just enough to book their place in the next round.
Craig Brewster was in the starting line-up against St Johnstone at Victoria Park – where the Perth side had lost heavily to Ross County six days earlier.
The first hint of a chance on goal came in the fourth minute when a Brewster shot was blocked, before Barry Wilson drove the rebound against former team-mate Paul Sheerin.
Caley were awarded a free-kick three minutes later and after Wilson's attempt was charged down, Liam Keogh blasted the loose ball well over the crossbar.
In Saints' first real attack Peter MacDonald crossed the ball for Michael Moore but he slipped at the vital moment and the chance was lost.
Then MacDonald flashed one past the upright as the visitors came more into the tie.
There was little between the teams with few openings in front of goal and Caley were restricted to long-range shooting when Wilson tried his luck in the 21st minute, but his effort flew well over.
The best chance of the first half arrived four minutes later when a Sheerin cross was touched on by Sean Webb and Ian Maxwell crept in at the far post only to fire his shot wide of the opposite post.
Brewster was then in trouble with referee Dougie MacDonald for changing his boots without permission.
The tie got bogged down for a spell before the interval but it livened up when a MacDonald free-kick flew over the crossbar, and at the other end a Russell Duncan shot cannoned off the outside of the post and Ross Tokely fired the rebound over the crossbar.
Both teams found it difficult to find that something extra that would open up the tie, and the first real action after the break came from a surging run from Tokely that petered out before he could find the target.
Caley were finding another gear and Bryan Prunty failed to control a Brewster cross, then the same player was unable to get on the end of a Roy McBain delivery right in front of goal.
But it was Brewster who missed the best chance of all when he collected a pass from Wilson after Saints keeper Kevin Cuthbert made a hash of a pass back, but the player-boss amazingly slotted the ball past the right hand post with the goal at his mercy.
After a good spell of pressure Caley made the breakthrough when Duncan fed Tokely and his cross was headed home by Golabek from six yards.
Caley looked comfortable with their slender lead and substitute Richie Hart almost added a second eight minutes from time but he blasted over the crossbar from just inside the box.
Then Duncan was right through on goal, but Cuthbert made a superb point-blank save to deny the Caley Thistle player in the dying minutes.