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Hearts boss Craig Levein hailed his players for refusing to buckle to the pressure as they shrugged off first-half nerves to book their place in next month's William Hill Scottish Cup final.
The Jambos dominated the first 45 minutes at Hampden against John Robertson's Inverness but were booed off at the break by their own support after failing to capitalise.
It was the second time in a matter of days that the Gorgie faithful had turned on their team after seeing them lose to bitter rivals Hibernian in last week's Edinburgh derby.
But this time there was celebrations at full-time as goals from Uche Ikpeazu and John Souttar before substitute Sean Clare's penalty secured a 3-0 win and booked the club's first appearance in the final of the competition since their famous 2012 triumph.
Afterwards Levein praised his squad for holding their nerve to set up another Hampden clash on May 25 with the winner of Sunday's semi between Aberdeen and Celtic.
He said: "We've had a rollercoaster season but I'm so proud of the players, how they dealt with the pressure.
"The pressure was the thing that was against us. We had more ability than Inverness but we had more pressure and they had less ability and pressure, that's why we're favourites.
"Being favourites does make you worry sometimes about losing but they handled that very well and a result, of course, is us playing here in May."
Levein is just two years away from clocking up four decades worth of involvement in senior football – yet he has never won a major trophy.
Now the 54-year-old hopes his long wait will come to an end.
"It's a very proud moment for me," he said. "I've done a lot things in football but to come back and win a cup with Hearts would be the best thing."
Hearts' first-half struggles were quickly forgotten about as Ikpeazu turned the ball past former Jambos goalkeeper Mark Ridgers four minutes after the interval when Jake Mulraney fired a dangerous ball into the six-yard box.
Caley Thistle responded well but saw luck desert them twice as first Zdenek Zlamal produced a finger-tip save to force Joe Chalmers' free-kick onto the crossbar before the officials wrongly chalked off a wonder strike from defender Jamie McCart.
With those let-offs, Hearts pressed on and wrapped up the game. First Souttar pounced to net from an Olly Lee corner before Clare stroked home from the spot after Ridgers took down Ikpeazu.
Deflated Highlanders boss Robertson said: "I'm incredibly proud of my players, my fans and my club.
"The first 45 we did the job we needed to do, which was to keep Hearts quiet and quieten the crowd. They were booed off at half-time, which was exactly the reaction we were looking for.
"They got their goal from a set-play, which is difficult to take. It's a wee ricochet and they score.
"Then the little bit of luck you need for a Championship team to beat a Premiership team is what killed us.
"Chalmers' free-kick is incredible. The save from Zlamal is as good as I've seen all season. Finger-tips is all it was but he's got it onto the underside of the bar.
"Then the second bit of luck we need comes with the offside goal. It's not offside. Jamie McCart is offside but it's Jake Mulraney who plays the pass.
"That is again when you're hoping the officials pick that up. If you get one of them – or both – then all of a sudden it's a totally different match.
"Hearts then went and scored another set-play and it's game over."
