Steve MacLean found himself through on goal in the 25th minute, but he was hauled down by Laing, who joined on loan from Nottingham Forest this week.
He was adjudged to be denying a goal-scoring opportunity and therefore received his marching orders.
St Johnstone continued to press after the break, with MacLean sending a header inches wide after good work on the flank by Gary Miller.
The defender then saved his team a goal after clearing off the line following a Fraser Kerr header.
It was 10-man Motherwell who equalised against the run of play, with Dominic Thomas dribbling past three players before teeing up John Sutton, who smashed the ball into the top corner from 20 yards out.
The result leaves St Johnstone in sixth position, while Motherwell remain in 11th, six points ahead of basement side Ross County.