Ross Draper sent Caley Thistle on their way to their third consecutive SPL win with a free header from Graeme Shinnie's 13th-minute free-kick, and Antonio Reguero ensured that they went in ahead at half-time when he tipped over a Leigh Griffiths effort after a rare lapse in the home defence.
Inverness stepped up a gear after the break and Richie Foran bundled home David Raven's cross in the 76th minute before SPL player of the month Billy McKay headed home a late third from a cross by young player of the month Aaron Doran.
Butcher also won a monthly prize after closing November with victories at Celtic Park and Aberdeen and the Inverness manager was delighted to see his side carry on their form.
"It's another great win, a clean sheet, three goals - great for the goal difference," he said.
"It wasn't the best performance this season but it was very effective and very strong.
"It took time to get the second goal but when we did, we were comfortable. They were good goals, spread throughout the team.
"We said at half-time: 'Do the basics right'. When we won it in the first half we gave it right back.
"Our ball retention in the second half got a lot better but the second goal wouldn't come. But it finally did and then the third was the icing on the cake.
"We are second in the league and it's a heck of a feeling."