FOR Dunfermline Athletic, home is where the hurt is.

This was the 12th game to have been played at East End Park this season and Jim McIntyre's side have yet to win even one of them. Talk about a dirty dozen.

Not even a switch from the league to the cup, it seems, could bring about a change in their fortunes, Inverness Caledonian Thistle rallying from a goal down to earn a fifth-round Scottish Cup home tie against Celtic. It doesn't get any easier for Dunfermline in their bid to end this horrible sequence, either – their next home match is against Rangers early next month.

It took extra time to settle this replay, although it took only two-and-a-half of the 30 minutes for Inverness to forge back in front. Gregory Tade slipped a pass inside to Andy Shinnie and the midfielder cracked a drive into the far corner of the net via a post. A further strike by Greg Tansey in the second period killed off any prospect of a late Dunfermline fightback.

They may come to look upon Inverness's second-half equaliser as the turning point, another moment to forget for poor Chris Smith. With new signing Iain Turner ineligible, the former St Mirren goalkeeper – at fault for goals in recent games against St Johnstone, Celtic and the original tie between these two teams – was at least partially to blame for Inverness drawing level after 54 minutes.

Smith's confidence would surely not have been helped by the sarcastic cheers from his own fans whenever he made a routine catch or save and would have been dented further by the mix-up with Kevin Rutkiewicz, following a poor back-header by Alex Keddie, that presented Johnny Hayes with a tap-in from around six yards out.

Hayes, who similarly profited from a Smith error in the original tie, couldn't miss and so began yet another post-mortem in the Dunfermline defence. Unsurprisingly, they have not kept a clean sheet at home since the first match of the season. "It's happened one too many times this season," said McIntyre. "It's a hammer blow to the confidence and it handed them the initiative."

Given the cold conditions and the fact the match was shown live on television, as was Barcelona versus Real Madrid, it was perhaps not surprising that East End Park hosted Dunfermline's lowest crowd of the season, with only the main stand open. Those who ventured out of the house were rewarded with a scrappy cup tie with little quality beyond a handful of incidents. On a pitch that cut up badly the more the game wore on, perhaps nobody should have been that surprised there was little to get excited about.

Dunfermline have come to regret wasting chances in recent matches and they were similarly profligate here. Within the opening minutes Andy Barrowman had shot wide and then had another saved by Jonny Tuffey that the striker probably should have buried. He would have greater joy later in the half.

Martin Hardie had a couple of free-kick attempts similarly gobbled up, before Inverness finally troubled Smith with a Tansey shot that bobbled into the goalkeeper's arms. Then, with half-time approaching and the game descending into a midfield scrap, a goal. It was a rare bit of quality. Joe Cardle scurried down the left wing before sending in an enticing cross and Barrowman atoned for his misses by heading firmly past Tuffey.

Inverness emerged from the half-time recess with greater purpose, perhaps following an inspiring word or two from their manager.

The introduction of Andy Shinnie had an immediate effect, the midfielder setting up Billy McKay for a shot Smith saved well. Then came the Dunfermline defensive howler that drew Inverness level, imbuing the visitors with greater emphasis as the match wore on, although their eagerness seemed to boil over with team-mates Richie Foran and Hayes both picking up bookings for a shoving match in the middle of the park. Talk about fighting Irish.

"The referee took a good hit on the head, as well," said manager Terry Butcher. "I'm not sure how they did it but they hit a referee and got away with it. I never got away with that in my playing days. I had a go at Richie just to get Johnny going as he was frustrating. So Richie had a go at him and Johnny had a go back. Johnny after that was excellent."

There were chances for both sides to finish it within the regulation 90 minutes, most noticeably Ryan Thomson's effort for Dunfermline that Tuffey did well to repel from close range, while Smith also made partial amends for his part in the Inverness goal by saving from Andy Shinnie. But the former Rangers player would not be denied in extra-time, his fine strike as out of place in this contest as a polar bear in the desert, before Tansey sealed the win with a neat finish.