Goals from Michael O’Halloran and James McFadden fired Saints into an early 2-0 lead before the Staggies fought back after the break to reduce the deficit through Jake Jervis’s cool finish.
Both sides spurned a host of chances in the dying minutes as the game finished with the same scoreline as their Scottish Premiership encounter last weekend.
The home side made a dream start when McFadden’s free-kick in the fifth minute was deflected into the path of O’Halloran who slotted home despite appeals of off-side from County.
And they doubled their lead just six minutes later when former Everton star McFadden capitalised on a poor clearance and unleashed a curling effort from the edge of the box that flew beyond goalkeeper Mark Brown.
McFadden went close to adding a third shortly afterwards with a curling right-foot effort that flew inches wide of the upright.
The visitors got into the game and came close to reducing the deficit on the half-hour mark when Martin Woods’s effort from close range was saved.
And they were unlucky not to score when Frazer Wright nearly put the ball into his own net with a header which was brilliant kept out by Alan Mannus.
But St Johnstone continued to carve out the better chances with O’Halloran setting up Lee Croft whose goal bound effort was cleared off the line by Scott Boyd.
County improved after the break and came agonisingly close to scoring when Joe Cardle twisted past a few players but was unable to get his low effort on target.
Mannus was then called into action to tip over Reckford’s ferocious effort from just inside the area as the visitors continued to press.
And they deservedly pulled a goal back just after the hour mark when Jervis beat the off-side trap to coolly make it 2-1.
Jervis should have levelled matters a few minutes later after Filip Kiss’s brilliant pass but the striker could only poke his effort wide.
Saints then hit back and could have wrapped up the tie with Brian Graham rattling the crossbar with a half volley after racing onto Simon Lappin’s long ball.
The Cup holders then missed two more glorious chances with Dave Mackay firing a volley past the post, following a corner, before Graham somehow placed his shot wide with the goal at his mercy.
St Johnstone spurned another opportunity late on when David Wotherspoon raced onto Brian Graham’s pass and forced Mark Brown into a stunning save but they hung on for victory to book their place in the last 16.