Maclean struck twice in the first half as he took his recent goal tally to six in four matches, before Gary Miller added a late third.
The home side had to make do without defenders Frazer Wright and Tam Scobbie but dominated the game from the outset.
St Johnstone forced a couple of early corners but it was the away side who had the first chance through Henri Anier who fired wide.
But St Johnstone did not have to wait long to make a breakthrough. Maclean won a free kick in the sixth minute which was taken by Stevie May.
Faroe Islands goalkeeper Gunnar Nielsen saved but Maclean was on hand to tap in the rebound from close range.
Motherwell managed to muster a shot on target midway through the half but Iain Vigurs' effort from distance was saved low to his right by Alan Mannus.
Maclean almost notched his second shortly after but failed to find the target with a header from six yards.
But Maclean was not to be denied his second of the game after scoring again in the 35th minute, nodding in Brian Easton's inswinging cross.
Motherwell had a chance to pull a goal back on the stroke of half-time but Stephen McManus dragged the ball narrowly wide of Mannus' left post.
The home side came out of the traps quickly in the second half and nearly went three in front. Lee Croft blasted a shot at goal from a tight angle, only to be denied by Nielsen.
St Johnstone's top goalscorer May then fired a long-range shot at goal just before the hour mark but Nielsen was equal to the task, saving low to his right.
Nielsen was fast-becoming the busiest player on the pitch and was called into action again to deny Chris Iwelumo and Gary McDonald as the home side threatened to run riot.
St Johnstone added a third when Gary Miller struck three minutes from time firing across goal and into the left-hand corner.
It was an ideal response from Tommy Wright's men as they bounced back from a 1-0 defeat at Inverness Caledonian Thistle on their last league outing.