Fletcher opened the scoring midway through the half and Killen added the second from the penalty spot after he had been brought down by goalkeeper Mark Brown, who was sent off for his pains.
Killen lofted a 20-yard shot high over the top after a couple of minutes and Steven Whittaker was not far away with a terrific left-foot shot which cleared the far post.
Inverness were well organised and not afraid to take the game to Hibs and a John Rankin shot from distance was spilled by Zibi Malkowski but he recovered in time to prevent Craig Dargo cashing in.
Killen then saw a shot deflected over the top before a great run from Whittaker almost brought a wonder goal, but he was closed down at the last minute.
Brown pulled off a superb one-handed save to keep out a deflected shot from Michael Stewart as Hibs stepped it up before the interval.
But it was Inverness who came closest to breaking the deadlock after 42 minutes. Malkowski somehow got a hand to a Dargo volley and then produced an even better save to keep out Graham Bayne's follow up from no more than a yard out.
Roy McBain had a decent chance for Inverness early in the second half after a lapse by Whittaker but he shot tamely at Malkowski.
Rob Jones then cleared a Bayne shot off the line after Grant Munro had headed a Rankin cross into his path.
The breakthrough came in 65 minutes when Fletcher thundered in a 15-yard shot after David Murphy had headed the ball into his path.
Hibs almost added to their lead when a shot from Scott Brown struck Munro and then the top of the crossbar.
Killen then put the result beyond doubt after Brown had fouled him as he went round the goalkeeper and he slammed the penalty high into the net.