The home side made the brighter start and should have taken the lead as early as the sixth minute when Shaun Fagan sent Jim Hamilton clear but the striker somehow managed to send the ball wide from only eight yards with Mark Brown stranded.
Brown was called into action in the 21st minute when he tipped a Fagan long-range effort over the bar. David Clarkson replaced the injured Hamilton and he could only repeat the experienced striker's miss when he dragged a shot wide from a Richie Foran pass.
Motherwell found it hard to believe that their first half pressure saw the game still tied at 0-0! The game continued in the same vein at the start of the second half with Scott McDonald missing on a couple of occasions and a Brian McLean effort blocked by Brown.
A goal seemed inevitable but the only surprise was that it came from the visitors. Brewster's clever flick sent Craig Dargo clear and the striker steadied himself and fired the ball into the net through the legs of Smith.
Ten minutes later Smith pulled off a stunning save to keep his side in the game when he blocked an Ian Black effort at point-blank range. At the other end Motherwell continued to push for an equaliser and the closest they came was a Clarkson header that hit the post.
Inverness sealed their win with two minutes left when Richard Hart's cross found Dargo unmarked at the back post to sweep the ball into the corner.
Inverness boss Craig Brewster said after the game: "In the first half we were murder, we were second to every ball and Motherwell controlled the game. We were glad to get in at half-time still at 0-0.
"The second half we competed better and we were challenging for the second ball. When we scored I thought that there was only ever going to be one winner."
Motherwell manager Terry Butcher said: "That is the best we have played for a while, the only failure we had was putting the ball into the net.
" The longer the game went, however, it was inevitable that Inverness would get a chance and they took it."
Motherwell continued to push for an equaliser and the closest they came
was
a Clarkson header that hit the post.
Inverness sealed their win in the break with two minutes left when
Hart's
cross found Dargo unmarked at the back post to sweep the ball into the
corner.
Inverness boss Craig Brewster said after the game, "In the first half
we
were murder, we were second to every ball and Motherwell controlled the
game. We were glad to get in at half time with it still at 0-0.
"The second half we competed better and we were challenging for the
second
ball. When we scored I thought that there was only ever going to be one
winner."
Motherwell manager Terry Butcher said, "That is the best we have played
for
a while, the only failure we had was putting the ball into the net.
Although
the longer the game went it was inevitable that Inverness would get a
chance
and they took it."