Richie Foran's fourth-minute opener was added toin the 36th minute by Billy McKay - his third goal in as many matches this season, with Inverness producing a comprehensive attacking display in the opening 45 minutes.
After the interval, however, Caley Thistle were forced to defend under some pressure from Motherwell, but limited them to few chances as they ran out deserved winners, much to the delight of manager Butcher.
He said: "It was a good first half performance, but I felt that overall it was a game of two halves.
"We knew that with the wind in the second half Motherwell with get it forward to John Sutton, while they have good pace in their team.
"They caused us problems, but we defended well and showed a lot of grit, resilience and steel.
"That's the new mantra at this club - stamina, steel and style."