Goals in the first half at McDiarmid Park from Frazer Wright and two from Francisco Sandaza put paid to any hopes of the Irn Bru First Division side causing an upset.
St Johnstone, clearly buoyed by their weekend victory at Celtic, began brightly, Murray Davidson flashing a header just wide on seven minutes after a fine cross by Liam Craig filling in at left-back.
The hosts though only had to wait another five minutes for their opener.
Former Hibs goalkeeper Andrew McNeil spilled a cross from the right and from the resulting corner Wright bundled home his first goal for the club on the half-volley.
It was to be a night of firsts for St Johnstone and Cillian Sheridan nearly got his first goal since returning to the club but his sliding finish went just wide after good work down the right by Jamie Adams.
Livingston's first effort on goal came from Liam Fox after 16 minutes but his effort from 20 yards was well saved low to his left by Peter Enckelman.
Sandaza stretched Saints' advantage two minutes later with a fantastic turn and strike from the edge of the box after being fed by Willie Gibson.
Gibson was impressing on his debut having only finalised his loan move from Crawley earlier in the day and his free-kick from 25 yards had McNeil in trouble again but the keeper collected at the second attempt.
However, Saints were not to be denied and got their third of the evening after 25 minutes when a Paul Watson slip allowed Sheridan to run through and feed Sandaza who took his time before slotting low beyond McNeil into the far corner.
The only concern for Derek McInnes after a fine first 45 minutes from his side were injuries to Wright and Davidson which saw both withdrawn before the interval to be replaced by Alan Maybury and David Robertson respectively.
Livingston improved after the break but lacked a goal threat with Kenny Deuchar having been replaced at half-time.
Bobby Barr had an effort deflected wide and Iain Russell wasted the visitors' best chance when he pulled his shot wide with Keaghan Jacobs was better placed.
The visitors' improvement though was just as much to do with St Johnstone taking their foot off the pedal and the home side should have added to their total when substitute Marcus Haber miscued when trying to backheel the ball into the net after a cut-back from Sandaza.
Gibson came agonisingly close to capping his debut with a fine strike that went just over with the last kick of the game.