St Johnstone won at Fir Park to consign Motherwell to a second straight Scottish Premier League defeat.
An own goal by Tim Clancy gave Saints the advantage on 20 minutes, the defender helping a Jamie Adams header into the net.
Efforts from Steve Jennings and Tom Hateley failed to trouble goalkeeper Peter Enckelman as Well pressed.
And the visitors added to their lead with Francisco Sandaza and Liam Craig netting in the final 15 minutes.
The result extends St Johnstone's unbeaten run away from home to seven matches.
Sandaza and Motherwell midfielder Nicky Law both had early efforts saved.
Clancy drew a save from Enckelman with a glancing header from a corner, but it was at the other end that the Motherwell player broke the deadlock.
Craig's free kick was headed around the Motherwell box and Adams' nodded effort towards goal was turned into his own net by Clancy.
Sandaza headed Dave MacKay's cross wide before Jennings swept a shot over for Motherwell.
The hosts won a free-kick in a promising area near the end of the first half, but Tom Hateley's effort was too high.
Sandaza dragged a shot wide after skilfully escaping some Motherwell defenders in the opening minutes of the second half.
Enckelman flapped at a Steven Hammell cross but recovered in time to block Michael Higdon's volley.
Randolph ensured his side did not slip further behind when he palmed away Chris Millar's curling effort, Adams heading the rebound over.
However, the second goal was not long in coming as Hammell's wayward pass across his own defence was pounced upon by Sandaza and the striker rounded the keeper to convert.
Sandaza then turned Stephen Craigan inside out before unleashing a shot that Randolph blocked only for Craig to bury the rebound high into the net.