Danny Devine’s first goal of the season put Inverness through to the semi-finals of the Scottish Cup.
In a low-key encounter, Devine’s second-half header booked the Caley Jags their first trip to Hampden Park in more than a decade, against either Dundee United or Celtic.
John Hughes’ side will have to wait until March 18 to find out who their opponent is, when the replay takes place at Parkhead.
Caley Thistle made one change from the side that lost 2-1 to Motherwell 10 days ago.
Marley Watkins, who was suspended against the ‘Well, came into the side at the expense of Nick Ross. New signing Tarmo Kink was on the bench.
Inverness had the first two opportunities of the game, with Greg Tansey curling wide and Edward Ofere seeing a header blocked by Paul Watson.
With 14 minutes on the clock Ofere threatened again, meeting Danny Williams’ cross with a firm header, but again, he saw it blocked.
The hosts lost possession from the resulting corner and Raith broke on them. Only a toe from David Raven prevented Rory McKeown getting on the end of Mark Stewart’s cross.
In a game that was opening up for both sides, Ryan Christie set away Watkins on the break 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 came close again before the break, this time meeting a Christie cross and flicking wide of the far post.
The best chances of the first half came within moments of each other. First Graeme Shinnie saw his effort saved by David McGurn when one-on-one and when the following corner was cleared, Williams smashed the ball against the crossbar.
Watkins spurned a golden opportunity at the start of the second half. This time 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 ballooning over two opportunities to score.
The breakthrough finally came on 64 minutes when Devine, starting just his second game of the season, rose highest at the back post to head in Tansey’s corner off the woodwork.
In a laboured finale, Caley Thistle gave a debut to Kink, before seeing out the victory.