The Steelmen started off well and could have been one up as early as the second minute. After Phil O'Donnell and Scott McDonald had had shots blocked by Marvin Andrews, the ball broke to Brian Kerr and his effort struck the bar and went over with Ronald Waterreus beaten.
The home side continued to be the better side for the remainder of the half with Rangers presenting few problems in the final third.
In the 35th minute Rangers presented Motherwell with a gilt-edged chance when Waterreus flapped at a Kerr corner and O'Donnell headed back to McDonald but his effort was cleared off the line by Sotirios Kyrgiakos.
At the start of the second half Rangers looked more lively and Thomas Buffel blasted wide three minutes after the re-start.
This was followed by what turned out to be the only goal of the match. Rangers were award a soft free-kick by the erratic Kenny Clark. Robert Malcolm swung the ball into the box where Andrews' header found Peter Lovenkrands with all the time in the world to blast past Steven Smith from six yards out.
Well pushed hard for an equaliser but found Waterreus in inspired form.
Firstly he reacted well to keep out an O'Donnell flick in the 65th minute, and then followed that up with a stunning block from McDonald's close-range effort 11 minutes later.
Despite much late pressure Motherwell couldn't find the equaliser that their overall play deserved.