Clarkson's header gave Well boss Terry Butcher victory over his old adversary John Robertson, but although the Livingston manager was bitterly disappointed with the result and his team's performance, relegated Livi were actually the better side for much of the opening hour.
Robert Snodgrass missed the first real chance of the game after 13 minutes when Graeme Smith blocked the teenager's left-foot shot with his legs.
Defender Dave Mackay and Snodgrass again went close without bothering Smith as the home team continued to dominate against a strangely muted Motherwell line-up.
A Jim Hamilton back-heel set up Brian Kerr for a stinging low drive and youngster Mark Reynolds almost deceived keeper Roddy McKenzie with a hopeful high punt but that was the best the visitors could manage.
The turning point arguably came on the hour mark when former Celtic midfielder Colin Healy blasted the ball against Smith from barely five yards.
Motherwell suddenly woke up and, after Clarkson, Stephen McGarry and Hamilton had all threatened, Clarkson beat McKenzie to a cross from substitute Martyn Corrigan and nodded the Steelmen in front.
Jim Paterson then clipped the top of the crossbar as Motherwell confidently played out the closing stages.