Thistle put up some stuffy resistance in a fifth-round tie that had been postponed from Saturday and Tuesday because of a waterlogged pitch and heavy snowfall.
However, although they laboured to make the breakthrough with Murray Davidson's 42nd-minute opener, there was little doubt thereafter it would be the SPL side which would progress.
Substitute Liam Craig's stunning 30-yard drive put the icing on the cake for the home team, who will now fancy their chances of seeing off part-time Brechin in the next round.
The sodden pitch survived a lunch-time inspection, and it was Partick who settled first on the sticky surface that did not take long to churn up badly.
St Johnstone looked surprised by the way their visitors from a league below had begun the match, but gradually found their feet without managing to threaten Scott Fox in the Thistle goal.
The McDiarmid Park side were finally sparked to life by a flash of determination and skill from skipper Jody Morris, but unfortunately for the home team the former Chelsea midfielder was deep in his own half at the time.
Striker Collin Samuel then caused a moment of panic for the visiting rearguard when he turned and drove at the retreating band of defenders.
However, his shot from the apex of the box swung across Fox's goal and slipped past the upright by a couple of yards.
The Saints continued to huff and puff in and around Thistle's area without carving out even a half-chance to lift the sparse crowd of just 2,441 on a night when TV coverage of Scotland's friendly with Northern Ireland may have appeared a better bet.
However, they seemed energised as the interval approached.
Cleveland Taylor saw a hooked volley deflect into the arms of Fox and Samuel spurned a gilt-edged opportunity to make the breakthrough when he seized on a mix-up between Paul Paton and Willie Kinniburgh, but struck the post in a one-on-one with the Thistle keeper.
And four minutes before the interval, they finally found the breakthrough.
Taylor rattled in a speculative shot which deflected into the path of Davidson, who prodded the loose ball into the net from 10 yards out.
St Johnstone made what was to prove a key alteration at half-time, with Taylor making way for Craig. But it was Partick who had to make the biggest change after falling behind just before the break.
The Firhill outfit knew they would have to attack more than they did in the opening 45 minutes if they were to have any chance of working their way back into the tie.
However, it was the home side who came closest to the next goal in the 55th minute.
Craig latched onto Dave Mackay's ball into the box only for Paton to block his right-foot attempt from eight yards out.
But, after Fox then blocked at the feet of Samuel, Craig did extend Saint's advantage only two minutes later with a wonder strike from 30 yards out.
The former Falkirk midfielder latched onto a bouncing ball and lashed a magnificent dipping drive over Fox's despairing dive and into the roof of the net.
Thistle passed up a great chance to get themselves back into the game six minutes later when Chris Erskine sent a superb defence-splitting pass into the path of Paul Cairney.
But the striker's poor first touch took him too wide past advancing goalkeeper Peter Enckelman and he could not find a team-mate with the resulting cut-back.
Comfortable in their lead, St Johnstone took their foot off the gas and allowed their visitors more possession as the clock ticked down but there was never any threat of a late comeback.
An Enckelman clearance charged down by Martin Grehan was the closest the Glasgow outfit managed to get to a consolation goal as Saints saw out time with a bit to spare.