After 18 minutes Mark Corcoran could have put the home side ahead when he beat the offside trap, but Graeme Smith got a hand on the ball to take him wide from where he could only hit the post.
It was therefore no surprise when Saints took the lead after 22 minutes. The lively Corcoran robbed Martyn Corrigan and picked out Charlie Adam with his cross, and the on-loan Ranger side-footed past Smith from 12 yards.
Motherwell re-grouped and handled the Saints threat without ever looking like scoring themselves.
The second half started as the first finished with the visitors seeing plenty of the ball without ever looking like finding a breakthrough.
On the hour mark it was the home side who almost repeated the move which had opened the scoring with Corcoran beating Corrigan and Brian McLean, but this time his cross went behind Adam.
The half had a look of stalemate about it with both sides knowing the next goal would be crucial. After 73 minutes Saints won a free-kick on the left edge of the box, and Simon Lappin's cross was met superbly by the head of John Potter to leave Smith with no chance.
Saints put the icing on their performance when they grabbed a third in the 90th minute when John Sutton sent Adam through to crash a shot past the helpless Smith.
This was a well-deserved win for the first division leaders, who more than matched their SPL opponents in all departments.