They were grateful for three first half goals which allowed them to move four points ahead with two games in hand over their nearest rivals.
Motherwell got off to the best possible start when they opened the scoring in the seventh minute. Ross McCormack dinked a great ball into the box for David Clarkson, who killed the ball before firing past Mike Fraser from six yards out.
Two minutes later they doubled their lead and once again McCormack was involved as he held the ball up at the edge of the box before laying it back to Steven Hammell. The left-back's first time cross was perfect for Chris Porter to head home at the far post.
Inverness clawed their way back into the game on the 20 minute mark when Don Cowie fired a spectacular shot high past Graeme Smith after a cross had been half cleared to the edge of the box.
Motherwell restored their two goal advantage three minutes before the break and it was almost a carbon copy of the Inverness goal. This time it was Clarkson who volleyed a half-cleared ball from the edge of the box.
Both sides were denied by the crossbar at the start of the second period. Firstly it was Motherwell's Porter who beat the offside trap but could only send his left foot shot onto the bar.
At the other end Inverness defender Grant Munro was unlucky to see two headers rebound off the crossbar from successive Cowie corners.
From then on there was precious little to excite either set of fans apart from the referee having to be replaced after apparently pulling a muscle.
In the dying stages Inverness threw four men up front and were unlucky to be denied what looked a stonewall penalty when Keith Lasley appeared to trip Russell Duncan but the ref waived play on.