Ryan Christie’s 19th goal of the season eventually separated the Scottish champions from opponents against whom they had rattled in 30 goals without reply in their nine previous encounters.
It was Celtic’s 34th consecutive domestic cup-tie victory as they secured yet another trip to Hampden in next month’s Scottish Cup semi-finals with their quest for a quadruple treble firmly on course.
Saints can hold their heads up after a gritty and often enterprising display in which them briefly flirted with the possibility of upsetting the odds. But, like so many before them, they discovered that this Celtic side simply refuse to entertain the prospect of their vice-like grip on the country’s silverware being loosened any time soon.
Having been so comprehensively swatted aside by Celtic in most of the recent meetings between the sides, St Johnstone’s priority was to remain competitive and defensively robust for as long as possible.
To that end, there was plenty of encouragement for Saints boss Tommy Wright in the manner his players set about fulfilling that requirement.
They were tactically and positionally diligent as they looked to restrict the number of clear-cut chances Celtic could manufacture.
James Forrest has been the main source of Saints’ misery during that run of heavy defeats and the winger was unsurprisingly the first to ask questions of the home defence, cutting inside Scott Tanser and slipping a pass to Christie who curled a shot wide from the edge of the penalty area.
It was far from simply a rearguard action by Saints and they posed an early threat of their own when Matt Butcher dragged a shot off target after Fraser Forster’s unconvincing attempt to punch a Callum Hendry cross to safety.
Slick, incisive football was difficult on the heavy, sodden pitch but Forrest, Odsonne Edouard and Callum McGregor managed to combine neatly on the left to carve out a good opening in the 13th minute. McGregor’s low shot was gratefully gathered by Zander Clark after it initially looked as if the ball may squirm under the goalkeeper into the net.
There was another response by Saints three minutes later when Hendry guided a header just wide of Forster’s left-hand post from a David Wotherspoon free-kick.
Clark made a fairly routine save to hold an Edouard shot after the Saints defence was unable to properly clear a well dug-out cross by Greg Taylor.
But it was Forster who made the more difficult stops in the remainder of the first half as Saints gave as good as they got. The big Englishman had to back-pedal furiously to touch over a deflected cross by the impressive Drey Wright, then got down to his left to turn behind a stinging shot by the same player who had pounced on slack play by Christie.
From the resulting corner, Forster was called into action once more when he did well to touch over a looping header by Jamie McCart.
Neil Lennon’s side sought to step up the tempo at the start of the second half and began to create opportunities more regularly. Forrest dragged a shot wide of Clark’s right-hand post after a smart 1-2 with Taylor, then Edouard burst forward after a mistake by Jason Kerr but his normal composure deserted him as he sent a poor shot high and wide.
Clark saved well from Forrest, then Griffiths and Christie both missed the target from inviting positions as Celtic enjoyed some sustained domination for the first time in the contest.
The increasingly busy Clark kept Saints in it with a couple of exceptional reaction saves, first of all from Christie’s close-range shot and then from a cute backheeled attempt by Edouard which the keeper somehow diverted on to his left-hand post.
The hosts looked to have ridden the storm and had another decent spell of their own during which Forster had to sprint from his line to prevent the hard-working Stevie May from getting on the end of a superb through ball by Ali McCann.
Just as it seemed the least Saints had earned was a replay, they were undone by a set piece in the 81st minute conceded by former Celtic defender McCart’s crunching foul on Forrest.
Christie’s fizzing delivery from the right was the kind defences dread and the ball sailed all the way beyond Clark’s right hand into the corner of the net. It looked as if Christopher Jullien may have got a slight touch to help it on its way but the celebrations indicated it was Christie’s goal.