Kilmarnock 2-0 Inverness CT
A double from substitute Paul Heffernan fired Kilmarnock into the last eight of the Scottish Cup.
The striker, on for the injured Cillian Sheridan late in the first-half, drilled in the opener on 58 minutes.
And the Irishman added a cute back-heel from Ross Barbour's strike with five minutes remaining.
Inverness, who lost Richie Foran and Andrew Shinnie to injury, forced a few saves from Cammy Bell but Ryan Esson was the busier of the goalkeepers.
Perhaps inspired by Friday's visit from American singer Marie Osmond, Kilmarnock started brightly and it took a sliding defender to block a shot from Barbour as the 20-year-old full-back broke into the penalty box.
Inverness, who lost in the League Cup semi-finals last weekend, were forced into an early change as skipper Foran hobbled off to be replaced by Philip Roberts.
Caley Thistle playmaker Andrew Shinnie picked out the galloping David Raven with a cute, chipped pass but the defender screwed his shot well off-target from 16 yards.
Kilmarnock forward Sheridan steamed his way into the penalty area from the left but his angled shot was weak and Esson, making a rare appearance for the visitors, made a comfortable save.
Home defender Jeroen Tesselaar was then left all alone at a free-kick but failed to get any meaningful contact on his attempted header and a glorious chance was spurned.
Inverness had to make a second substitution in the opening half hour, with the influential Shinnie apparently damaging a hamstring and Charles Taylor coming off the bench.
Roberts cut the ball back perfectly for Nick Ross near the penalty spot only for the Inverness midfielder to batter the ball against an opponent with a shot that lacked conviction.
Josh Meekings thought he had opened the scoring when he attacked an excellent corner from Aaron Doran but Sheridan was on the post to deny the Inverness centre-half with an instinctive clearance.
With the interval approaching, Kilmarnock pushed forward at pace to open up the Inverness defence but Sheridan's shot from 16 yards was woefully weak and Esson gathered with ease.
That was to be Sheridan's last contribution as he too pulled a hamstring and trudged down the tunnel to be replaced by match-winner Heffernan.
The second half opened with Bell making a smart save to prevent what would have been an own goal from James Fowler as the ball skidded off the defender's head from a corner.
Heffernan headed wide from a swift counter-attack but made amends with a lovely finish for the opening goal.
The visitors were outnumbered at the back as four Kilmarnock players surged forward and the ball ricocheted off two defenders as it broke to the substitute on the edge of the penalty area.
That may have been a touch fortunate but there was nothing lucky about the striker's emphatic, low finish.
With gaps appearing in the Inverness defence, Esson pushed away an awkward, bobbling shot from William Gross and recovered to make a great close-range block from Borja Perez.
Inverness struggled to create openings but Owain Tudor-Jones got his head to a corner, with Bell doing well to hold on to the ball.
And Heffernan made sure of Kilmarnock's deserved progress, diverting Barbour's low shot with his heel from six yards.