The visitors faced an uphill task after their goalkeeper was shown a straight red card early on for handling outside his area, stopping Calumn Hunter’s net-bound effort.
From then on there was no stopping Caley, as lethal marksman Chris Jones bagged a first-half hat-trick. The Liverpudlian lobbed Thorniewood’s stand-in keeper for his first, before powering in a header from Nick Byrne’s corner-kick.
The striker completed his treble when he controlled Spaniard Jordi Abelló’s cut back and fired in from close range.
The theme of the opening half continued after the break as Hunter sent in a diving head after an inch-perfect cross from Abelló. Abelló, playing his final game for the club before returning to Spain, bowed out in style when he danced past two defenders before sending a rocket strike careering into the net.
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Caley will be joined in the hat for the fifth round draw with Wallyford Bluebell after they enjoyed an emphatic 5-1 victory at home to Barrhead United.
The Premier Division outfit came from behind to win after they fell behind midway through the opening half.
Chris Moffat ensured Bluebell would go in level at the interval when he headed in Pinkie Tufail’s cross across goal and into the net.
Wallyford started the second half on top, and it wasn’t long before they took the lead. Ten minutes after the restart it was Moffat who was taking the acclaim of his team-mates again as he struck from 12 yards after Jordon Burrows strode up the right and cut the ball back to him.
Burrows bagged their crucial third when he tapped in after Barrhead’s goalkeeper had spilled an effort from range.
With the visitors throwing players forward as they tried in vain to get back into the tie, this left them susceptible to the counter-attack and it was via this route that Wallyford killed off their hopes with Burrows and Shaun Moffat netting.
Pentland Athletic and Tranent are also through to the last-16 after victories over Airdrie Albion and Coltness United.