The Englishman's appointment as new Hibs boss is expected to be confirmed in the next 48 hours, and he watched the action from the main stand at Easter Road.
Butcher's current team appeared determined to persuade him to remain in the Highlands, as quick goals from Nick Ross and Billy McKay set them up for victory.
Caley Thistle opened the scoring with a penalty from Ross (14) after James Collins pushed Graeme Shinnie in the back.
Four minutes later Shinnie burst forward again and slipped the ball to Billy McKay to finish from an angle after skipping past Ben Williams.
The visitors should have extended their lead further when Aaron Doran attempted to pick out McKay at the back post and Alan Maybury's interception came off his own post to Hibernian's relief.
Hibs tried to haul themselves back into the game and Paul Hanlon nodded wide from a corner shortly before the break.
Inverness came close again when a point-blank header from Marley Watkins was blocked by Hibs keeper Williams.
At the other end, Shinnie was called into action to clear a Collins header off the line as Hibs showed some spirit.
But Caley Thistle never looked like losing their early advantage as they climbed to second place in the Scottish Premiership table.