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Inverness Caledonian Thistle 1-0 Raith Rovers
Inverness Caledonian Thistle saw off Raith Rovers to set up a Scottish Cup semi-final meeting with either Celtic or Dundee United.
The hosts bossed possession and territory for most of the match, with Marley Watkins and Danny Williams both going close.
And Danny Devine nodded home the winner from Greg Tansey's corner after the break.
Visitors Raith never looked like getting back into the match.
The quarter-final victory means Inverness will face the winner of the replay between Celtic and Dundee United, which takes place on 18 March at Celtic Park.
The hosts had the first two opportunities of the game, Tansey curling wide and Edward Ofere having a couple of headers blocked.
Raith broke upfield from an Inverness corner and only a challenge from David Raven prevented Rory McKeown getting on the end of Mark Stewart's cross.
Inverness midfielder Ryan Christie freed Watkins and even though he was forced wide, he managed to arrow a shot right across the face of goal.
Although Inverness were comfortable in possession they lacked a killer edge in front of goal, often trying to do too much as simple passes and shooting opportunities were overlooked.
They also had trouble springing the offside trap with Ofere and particularly Watkins caught out by Raith's high defensive line.
Nigerian forward Ofere went close again before the break, this time meeting a Christie cross and flicking it wide of the far post.
The best chances of the first half came within moments of each other. Graeme Shinnie's effort was saved by David McGurn and, after the resulting corner had been cleared, Williams smashed the ball against the crossbar.
Watkins spurned a golden opportunity at the start of the second half. He beat the offside trap to get on the end of Josh Meekings' cross to the far post, but from four yards out the Welshman managed to turn it over the bar.
A pair of headers from Watkins and Meekings were tipped over the top by McGurn as the home side strived for the opening goal. Clear-cut chances to test McGurn were few and far between, however, with Christie twice firing over the bar.
The breakthrough came when Devine, starting just his second game of the season, rose highest at the back post to head Tansey's corner in off the woodwork.