A goal in each half from Don Cowie and Ian Black settled it and they also had goalkeeper Ryan Esson to thank for saving a second-half penalty.
Inverness dropped goalkeeper Michael Fraser after the heavy defeat at Ibrox and Esson took over between the sticks.
Hibs were first to show with Derek Riordan lashing a low 25-yard shot a yard wide of Esson's right-hand post after only 90 seconds.
But the home side struggled to get in behind a well-organised Caley Thistle defence and were increasingly frustrated.
Rob Jones saw a header across goal scrambled away by Black at the far post as Hibs' best chance of scoring looked to be from a set-piece.
Jones managed to get his head to a Riordan corner but Ross Tokely managed to get his head in the way and Inverness survived.
But Caley Thistle took a shock lead after 30 minutes. David Van Zanten let a long through ball from Black bounce in front of him and Cowie accepted the gift, as he steered a left-foot shot past Yves Makalamby.
Hibs failed to muster much in response and left the field at half-time to a chorus of boos from their fans.
Hibs were forced into a goalkeeping change at half-time with Makalamby picking up a first-half injury and Steve Pinau also came on for Steven Fletcher, who also took a knock.
Sol Bamba almost equalised in the opening minute of the second half with a low shot which Esson turned past his post.
But Caley Thistle doubled their lead moments later then Black gathered a pass from Cowie at the edge of the area and had time to look up and beat Andrew McNeil with a well-placed shot.
Esson was well positioned at the other end to hold a head-flick from Jones after Riordan curled in a free-kick.
Cowie had a chance for Caley Thistle after Garry Wood put him in but he dragged his shot across the face of the goal.
Hibs missed a penalty in 69 minutes when Esson pulled off a great save from Riordan after Richard Hastings had fouled Colin Nish.
The goalkeeper excelled again later in the half when he got down to his left to block a free-kick from Riordan.
Riordan pulled back a goal deep into injury-time when he hooked the ball home from close range but it was too little too late.