The visitors were indebted to goalkeeper Mark Gillespie for a man-of-the-match performance that moved the 'Well above Aberdeen into third place.
The first half was devoid of any goalscoring opportunities as both sides determination not to lose seemed to curb any attacking intent.
Motherwell should have gone ahead after 52 minutes but were prevented by a moment of complete selfishness from striker Christopher Long.
Hylton collected the ball on the edge of the area and curled a low shot towards goal that Laurentiu Branescu fumbled but with the ball rolling over the line, Long stabbed it home despite being blatantly offside.
There was a sense that only a mistake or a moment of genuine quality would prove decisive in an evenly matched encounter.
That moment arrived in style after 67 minutes courtesy of the left-foot of Motherwell's Carroll.
After Mark O'Hara was fouled by Niko Hamalainen, Carroll stepped up and sent a deliciously curled free-kick into the top corner from 25 yards out.
Kilmarnock, who sacked manager Angelo Alessio in midweek, pushed for an equaliser and Chris Burke's free-kick was punched cleared by Mark Gillespie before Brophy volleyed the rebound straight at the Motherwell goalkeeper.
Scotland international Brophy has struggled for form this season and he spurned a glorious opportunity on 77 minutes. After an intricate passing move, Stephen O'Donnell picked out his international colleague with an excellent cut-back but Brophy blazed wildly over from eight yards out.
It proved to be one of those days for the Ayrshire men as they couldn't find a way past the impressive Gillespie. The Englishman produced a stunning one-handed save to deny Brophy on 81 minutes.
The visitors should have sealed their win in the dying stages as substitute Liam Polworth raced clear but he ignored team-mates to fire straight at Branescu.
With virtually the last kick off the ball, O'Donnell was denied yet again by a wonderful left-handed save from Gillespie.