John Sutton’s penalty and a Gary Warren own goal put Motherwell in control at half-time, and Graeme Shinnie’s second-half reply failed to prevent a home win as the home side clung on at the end.
The result means Motherwell will go to Pittodrie on Sunday trailing second-placed Aberdeen by a point and in the hunt for a second successive runners-up finish.
A gentle night’s work appeared on the cards when Ross Draper dithered in the box four minutes in, was robbed by Sutton and hacked down the striker in an effort to atone for his error.
Sutton did the rest from 12 yards, and Motherwell were 2-0 up just after the half-hour thanks to another helping Inverness hand.
Warren was the benefactor this time, his attempt at a diving headed clearance only diverting Iain Vigurs’ corner into his own net.
Lionel Ainsworth was close to a third before the break, but Shinnie’s deflected reply 10 minutes after half-time gave the visitors a head of steam.
Greg Tansey and Billy McKay both went close as nerves began to affect Motherwell, and in the dying seconds McKay rolled a shot against the inside of a post with Lee Hollis beaten.