The Highlanders had failed to win any of their first seven Clydesdale Bank Premier League games and were languishing second-bottom when Dundee United visited Tulloch Caledonian Stadium at the end of September.
A shock 4-0 win for the home side, thanks to a first-half double by skipper Richie Foran and goals after the break by Andrew Shinnie and Philip Roberts, stopped the rot.
Inverness have since lost only one game in 16 and, as well as climbing to second in the SPL behind Celtic, have booked a Scottish Communities League Cup semi-final clash against Hearts and reached the latter stages of the William Hill Scottish Cup.
Butcher recalls the day when his side's fortunes turned.
He said: "Dundee United started off the game pretty well and for the first half an hour it was nip and tuck and then all of a sudden Richie scored two goals that have us a good half-time lead and we were able to build on that in the second half and run out 4-0 winners.
"We actually played well in the first seven games and had five points but hadn't had a win.
"We played well in some of those draws and were unlucky not to get the first victory but when the first win did come against United it certainly lifted everybody.
"It made everybody more confident, we had more belief and we knew that we were on the right track.
"We had a couple of wins right away after that and we zoomed up the table and we haven't looked back since then.
"So it might have been the turning point, the spark that we needed, but it was certainly welcome.
"It is nice to be able to play them again and it does whet the appetite."
Butcher, who has no fresh injuries following the win over the Staggies, is looking to give his far-travelled fans more to cheer about with another win.
The former Motherwell boss said: "I have a good relationship with my away fans and I am looking forward to seeing them because they are just phenomenal.
"They are so noisy and get behind the team.
"Man for man, I don't think there is a noisier away crowd so we are really pleased with the support we get from the away fans and it has been nice to reward them with some good away victories and points."