The Celtic fans were in rapture, the home fans in utter shock.

With 88 minutes and 30 seconds on the clock, Caley Thistle of "go ballistic'' fame, who twice in the last seven years had sensationally ousted Celtic from the Cup, were deservedly 1-0 up, courtesy of Graham Bayne's first-half strike, and heading for a third famous win over the Glaswegian giants.

Then, from a corner, the visitors snatched what seemed like an inevitable draw, Steven Pressley nodding in Stephen McManus's header back across goal. The celebrations ran into injury time, and there were only seconds of the two added minutes remaining when Kenny Miller smashed home the winner to break Caley hearts.

"It's just the belief we have in this team,'' said Miller, explaining his side's never-say-die attitude. "We didn't panic, we kept patient, we kept probing.'' Caley's manager, Charlie Christie, said afterwards that some of his players were in tears. "A draw would have been sore enough to take,'' he said. "I just didn't see this coming.'' Celtic go into Thursday's semi-final draw along with Hibernian (who won at Queen of the South on Saturday), Dunfermline (who beat Partick) and the winners of Motherwell and St Johnstone, who play on Wednesday.

Celtic started with Miller alone up front. He had a chance in the third minute when through on goal but Michael Fraser touched the ball away. Mark Wilson's lacklustre cross-shot soon afterwards was as potent as Celtic got until well into the second half.

Caley were intent on soaking up pressure and then hitting on the break, a tactic that worked when Ian Black, Barry Wilson and Bayne combined for the opener. Black was pivotal throughout. For the goal he placed a diagonal pass to Wilson, who squared for Bayne to score. Another Black-Bayne move also ended with the ball in the net 10 minutes later but it was ruled offside.

Caley held firm for most of the second period, threatened only by Shunsuke Nakamura walloping a shot against the underside of the crossbar. Gordon Strachan added fresh legs with three substitutes, one of them a 17-year-old Irish debutant, Cillian Sheridan. He combined with Miller for the goal. "I was thinking by then that maybe this wasn't going to be our day, " Strachan said. Yet it was, again.

Goals: Bayne (18) 1-0; Pressley (89) 1-1; Miller (92) 1-2.

Inverness (4-4-2): Fraser; Tokely, Dods, Munro, Hastings; Rankin, Black (McSwegan, 77), Duncan, McBain (Hart, h-t); Wilson (McAllister, 87), Bayne. Substitutes not used: Ridgers (gk), McCaffrey.

Celtic (4-5-1): Boruc; Wilson (Sheridan, 74), Pressley, McManus, Naylor; Nakamura, Hartley, Lennon, Sno (Gravesen, 79), Jarosik (McGeady, 65); Miller. Substitutes not used: McGovern (gk), Telfer.

Referee: D McDonald (Scotland).

Booked: Inverness: Wilson, Black.

Attendance: 7,119.

Man of the match: Black.