While Jack netted for the first time since April 2012, there were increasingly worrying signs as the match wore on that his defensive team-mates were in the mood to capitulate.
The game's other talking point centred on the dismissal of St Johnstone substitute Steven MacLean after he collected a second booking in the final minute, with McDiarmid Park manager Tommy Wright insisting referee Willie Collum had called it wrong.
"It was a poor decision," Wright said. "It was a mistimed tackle. If we're going to send people off for a second foul like that every time, you'll end up playing seven-a-side.
"It was like he couldn't wait to get the card out. Had he taken a few seconds to reflect on the challenge, he might not have given a yellow."
Jack's goal was the result of making space for himself after he received Peter Pawlett's square pass 25 yards out and placed his low shot into the St Johnstone net as visiting goalkeeper Alan Mannus failed miserably in his attempt to reach it.
Michael O'Halloran, the former Scotland under-21 international who joined the Perth club in January following three uneventful years at Bolton Wanderers was given his first league start and produced an industrious display as well as a stunning 18-yard shot that ricocheted off an Aberdeen post.
But although Jack's strike may have sent shivers down St Johnstone's spines as they recalled the events of Tynecastle a few weeks earlier when Aberdeen put four goals past them in the League Cup semi-final, they were resilient enough to withstand some first-half pressure before showing that they could threaten the opposition defence.
Indeed, had Lee Croft connected properly with his shot as he raced in on goal and had David Wotherspoon not sliced his close-range effort wide, the complexion of the game could have been so different.
Worrying for the home support was the disintegration of the Aberdeen midfield and defence as the Perth side's play meant the second half evolved into something quite different to the events of the first.
"Our energy levels weren't quite where they normally are," McInnes said. "The players worked extremely hard to get us across the line, but I take responsibility for not freshening up the team more than I did.
"We've had a lot of travelling in recent weeks and a tough game against Celtic in midweek. Matches against them always take that bit more out of you.
"St Johnstone got themselves into good positions and will be kicking themselves that they didn't manage to make more of that. But we've had 18 clean sheets and that shouldn't be sniffed at."
Wright, meanwhile, felt aggrieved that he left the north-east empty-handed.
"The least we deserved was a draw," he said. "I don't know how we didn't get anything from the game. We totally dominated the second half and we have to take the positives from that but ultimately we gave away a soft goal and the bad luck we had in front of goal cost us a point.
"We created enough chances to get something. The performance was great and I'm gutted for my players.
"We created so many chances against one of the best sides in the country and if we keep that up we'll make the top six."