Sandaza wrapped up three SPL points when he pounced on Stevie Hammell’s poor pass to put Saints two ahead with 15 minutes left.
The visitors looked comfortable after Tim Clancy’s 20th-minute own goal and further extended their lead through Liam Craig.
St Johnstone have now kept clean sheets in all four away games and added the emphatic win over a team sitting in third place to their surprise victory at Celtic Park.
Sandaza followed up his cup hat-trick against Livingston and double against former club Dundee United with another impressive showing, having a major hand in Craig’s late goal.
Motherwell had only lost against the Old Firm beforehand but even in those heavy defeats they managed to show some of the fluent passing that has been central to their excellent start to the campaign.
But they struggled in possession after the opening goal and could not break through St Johnstone’s disciplined ranks.
Motherwell started with Jamaica winger Omar Daley on the bench following his midweek signing with Chris Humphrey starting in place of the injured Shaun Hutchinson.
David McCracken and David Robertson dropped out for St Johnstone with Steven Anderson and Kevin Moon coming in.
Both teams tested the opposition goalkeeper from long range in the opening minutes. Darren Randolph pushed over former Motherwell striker Cillian Sheridan’s powerful strike and Peter Enckelman held Nicky Law’s similar effort at the second attempt.
Motherwell quickly gained control of possession and put together some good passing moves without carving a chance, although Enckelman saved Clancy’s glancing header from an inswinging Tom Hateley free-kick.
Saints took the lead when Motherwell failed to deal with Craig’s free-kick from the right. Jamie Adams headed the ball towards goal after Dave Mackay had headed it back and Clancy could only help it into the net from inside the six-yard box.
The goal seemed to rob Motherwell of their passing rhythm and they became over-reliant on hitting the ball long for Michael Higdon, who was struggling in the air against Frazer Wright.
St Johnstone were getting men forward on the break and Sandaza headed wide from Mackay’s cross.
Motherwell did enjoy some pressure late in the first half but could not test Enckelman.
Humphrey’s positive run and composed pass inside set up Steve Jennings on the edge of the box but the midfielder swept his shot two yards over and Hateley curled a free-kick on to the roof of the net.
Sandaza rode several tackles before pulling a shot wide from 20 yards just after the restart, but Motherwell were quickly on the offensive.
Enckelman flapped at Stevie Hammell’s cross but recovered in time to block Higdon’s volley.
The hosts failed to sustain the pressure though and Randolph kept them in the game with an excellent flying save in the 59th minute to stop Chris Millar’s curling effort finding the top corner after the midfielder had turned inside Hammell. Adams followed in for the rebound but could not readjust his body and headed over.
Daley came on for the below-par Jennings in the 72nd minute, allowing Law to adopt a more central position with the debutant lining up on the left wing.
The game moved beyond Motherwell three minutes later though.
Hammell received the ball back from Daley and played a square ball across his back line, but it failed to find its target and Sandaza emerged with the ball from Randolph’s challenge before slotting home from 12 yards.
Daley flashed a long-range shot wide but the visitors moved further ahead in the 85th minute.
Sandaza turned Clancy and forced a save from Randolph before Moon laid the ball off for Craig to finish high into the net.