Well manager Mark McGhee left the fit-again Ross McCormack on the bench, while Steven McGarry, Dave Clarkson and Chris Porter formed a three-man strikeforce.
Kilmarnock still had James Fowler sidelined due to damaged ankle ligaments, but forward Danny Invincibile returned after groin surgery.
A hamstring strain kept Garry Hay out of the action, while Craig Bryson had been ruled out for around one month due to a knee injury.
The opening minutes at Fir Park saw few openings for either team, before the home side broke the deadlock midway through the first period.
Clarkson was the man on target, slotting the ball past Alan Combe from Phil O'Donnell's assist.
A Colin Nish header just past the half-hour mark was Killie's best effort, but the visitors failed to offer much of an attacking threat during the opening 45 minutes.
After the restart, Well continued to make most of the running with Killie boss Jim Jefferies soon throwing on both Gary Wales and Gary Locke to try and change the pattern of the play.
McCormack entered the fray for the Steelmen soon after, but it was the visitors who struck the next blow, drawing level on the hour mark.
Locke's corner from the right found the head of David Lilley and he powered the ball past the stranded Graeme Smith.
Substitute Paul Quinn threatened to put Well back in front midway through the second period, with Combe making a smart save to keep the scores level.
Smith excelled at the other end to push a Jamie Hamill drive around the post, before Combe came to the rescue again as he blocked a Marc Fitzpatrick shot with his legs.
Veteran Combe denied Stephen Craigan as time ticked away and his efforts were repaid in full in stoppage time as Wales set up Dodds to drive home a decisive strike for Killie.