Jake Carroll also scored his first goal for the club as St Johnstone conceded from three crosses. The left-back netted from the rebound in the 72nd minute after Ladbrokes Premiership bottom club Saints threatened to get back into the game.
The first 20 minutes were a non-event with St Johnstone sitting deep and being unable to capitalise when Motherwell conceded possession in their own half on several occasions.
The wide man made the difference in the 29th minute when he turned his man near the bye-line and stood up a cross for Cole to nod home from close range to make it four goals in nine matches for the striker.
Motherwell came close just before the break when Hartley's header was cleared off the line from Liam Polworth's corner.
They scored from the same source inside four minutes of the second half when the home skipper attacked the midfielder's delivery to power home a header.
Cole fluffed a good chance to put the game out of sight after bursting through the middle and the visitors came back into it.
Ali McCann and Kane also failed to hit the target from decent opportunities before Tommy Wright made a double substitution midway through the half and changed to two up front with Michael O'Halloran joining Kane.
McCann soon drilled inches wide from long range and Zander Clark kept Saints in the game with a decent stop from Hylton's curling effort.
But the hosts soon moved out of sight after a 72nd-minute corner. Declan Gallagher's looping header bounced off the post and Carroll was on hand to force home the rebound.
Saints defender Wallace Duffy was forced off with a knee injury after going down under no pressure.
And there was further misery for the visitors when French striker Manzinga, whose debut was delayed by a hamstring injury, finished confidently after O'Hara headed on Scott's lofted pass.