But what little hope they did bring was crushed by a desperately flat performance by the home side, who scored a surprise goal after four minutes and pretty much went downhill from there.
As a consequence, St Johnstone mopped up a workmanlike win that should give them confidence for next weekend's Scottish Cup semi-final clash with Aberdeen.
Yet the Perth outfit would be well advised to go forward with caution, as Aberdeen are unlikely to be as ruinously dozy in defence as Kilmarnock were here.
The Dons can probably be relied upon to string more than two or three passes together as well, a feat that was quite beyond Kilmarnock. In possession, the Ayrshiremen dithered hopelessly at times, although there has to be some sympathy for those who tried to make things happen. As a rule, fluid football only tends to happen when team-mates are occupying the same postcode.
Kilmarnock were eager enough, but St Johnstone found them easier to read than Spot's First Wordbook. If there was a surge of excitement among the home supporters when Alexei Eremenko or Rory McKenzie broke from midfield, it was balanced by the near certainty that their efforts would come to grief near the edge of the box.
That pattern was broken only once, when McKenzie shoved a pass through to Kris Boyd, whose parried was shot was hammered home on the rebound by Robbie Muirhead for their early goal. In fairness, Kilmarnock were probably the better side until the clock passed the 20-minute mark, but the tide turned gradually and it became only a matter of time before St Johnstone were back on level terms.
That moment arrived in the 31st minute. By then, St Johnstone's crisper movement around the box had already begun to set the Rugby Park alarm bells ringing, and the threat finally registered on the scoreboard when Lee Croft rifled a corner in from the right side and Craig Wright timed his near-post header brilliantly to give Craig Samson, in the Kilmarnock goal, no chance.
It was a clear lesson for Kilmarnock, but not one they were inclined to learn. Thirteen minutes after Wright's header, St Johnstone won another corner, on the opposite side of the pitch, and the home side were caught out at the near post again. This time it was Steven Anderson who got the outside of his right foot to the cross from David Wotherspoon to leave Samson planted once more.
"We haven't scored enough goals from set plays this season," said St Johnstone manager Tommy Wright. "But we had two great deliveries and the two lads showed a lot of determination and desire to get ahead of their markers. It was no more than what we deserved.
"I thought we passed the ball really well and controlled large chunks of the game. If I'm being critical we probably should have scored more goals. You're never comfortable at 2-1."
Maybe not, but you're sitting a lot prettier than the side at the wrong end of that scoreline. The result keeps Kilmarnock mired in the relegation play-off area, and their anxiety seemed almost palpable in the closing stages.
"To lose two goals as cheaply as we did is very frustrating," said their boss, Allan Johnston. "Twice they showed more desire to get in front of our players.
"At the opposite end they were getting to our set pieces first, putting their bodies on the line. That's what you've got to do."