Teenager Jamie Murphy opened the scoring for the visitors with a 13th-minute header and Clarkson then contributed a goal in each half for Motherwell.
Substitute Stephen O'Donnell, making his comeback from injury, sparked a late rally when he scored with a fine volley, but it proved a mere consolation as the Paisley side remain mired in the relegation fight.
Andy Dorman had the first sight of goal after six minutes when Mark Howard's goal-kick was flicked on to him by Billy Mehmet, but as the St Mirren midfielder bore down on goal, visiting keeper Graeme Smith came out to make a good block.
Stephen McGinn was first to react to the loose ball as he raced in on the left side of the box, but Brian McLean booted his effort off the line at the near post.
Dorman then fired in a 30-yard free kick from near the right touchline but Scott Cuthbert headed over in a busy penalty box.
Motherwell had strung together some good passes but were unable to trouble goalkeeper Howard - until they took the lead after 18 minutes.
A Jim O'Brien corner was cleared and eventually found its way back out to Steven Hammell on the left flank, and he crossed into the box for youngster Jamie Murphy to head home a diagonal effort into the bottom left corner.
Dorman then swept in a cross from the right for Mehmet, arriving in the centre of the box, but his shot was easy fare for Smith.
St Mirren earned a succession of free-kicks not far from the penalty area in the second quarter of the game, and one such effort shortly before the half-hour was chipped by Dorman to the far post, where John Potter nodded narrowly wide.
Motherwell doubled their lead after 31 minutes when Stephen Hughes cut in from the right and drilled a shot which struck the base of the opposite post, and fellow Scotland B international Clarkson won the short race to the ball and tapped home the rebound from no more than a yard.
The recalled David Barron tried a cross from the left edge of the area, to which goalkeeper Smith seemed to get his fingertips as it dropped perilously close to the crossbar.
At the other end, Cillian Sheridan's ball from the byline had Howard scrambling to gather it on the ground and Clarkson sent a curling shot wide of the right-hand post.
St Mirren made an interval change, with Will Haining coming on to replace Jack Ross in defence.
The hosts won an early corner which was played down the line to McGinn, with Smith punching away his rising cross.
Hughes went on a run from midfield after 53 minutes and tried his luck with an effort from just outside the area, but the Motherwell midfielder's shot flew harmlessly wide.
Mark Reynolds needed attention on the pitch after colliding heavily with his own goalkeeper as they pursued and dealt with a ball to the right-hand post.
The visitors increased St Mirren's woes when they made it 3-0 on the hour.
The fit-again Paul Quinn floated in a cross from the right and although it went over the head of the jumping Sheridan, Clarkson was on hand to head home his second goal of the game from inside the six-yard box.
Home manager Gus MacPherson responded with an immediate double substitution, withdrawing McGinn and the recalled Dennis Wyness in favour of O'Donnell and Garry Brady.
St Mirren had looked unlikely to reduce the deficit in a lacklustre second-half showing, but they finally pulled a goal back as the game entered its final quarter.
A cross from the right found O'Donnell in the centre of the box, and just 12 minutes after his introduction, he sure-footedly met it first time and lashed home an impressive volley.
Smith thwarted Dorman when he tried to bundle home a cross and Mehmet protested loudly when he was challenged by Brian McLean on the edge of the box with nine minutes to go.
O'Brien had the last chance of the game when he thumped a promising effort wide in injury-time.
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