It was, to be fair, a Champions League-quality goal from James Brown – the first of his career – that set St Johnstone on their way near the end of the first half. Nicky Clark clipped home a second after 62 minutes and suddenly Rangers were staring an unthinkable defeat in the face.
There was still plenty of time left. The mark of an Old Firm side has often been their ability to keep going until the very end.
Celtic, after all, had scored twice in the last few minutes against Dundee United the previous afternoon to secure three points – they also took the points at this very ground with a stoppage time goal last month.
James Tavernier did cut the deficit after 74 minutes. John Lundstram cracked a 25-yard shot against the bar soon afterwards. He also grazed a post with a shot.
However, a strange acceptance appeared to settle over Rangers in the latter stages. It was as if they knew the game was up, and they could no longer paper over the cracks that have been appearing in a domestic setting.
Europe was, of course, another matter entirely. Freshly established as the worst-ever Champions League team, this was another embarrassing – and some would contend unacceptable – outing.
The booing from the away fans was sustained at half time as well as at full time, with Rangers' efforts having simply petered out.
Another corner, their 20th of the game, came to naught. St Johnstone broke up the park and substitute Connor McLennan took the ball into the corner, where he won a throw in.
Referee Steven McLean then blew his final whistle to signal a hugely significant win for the hosts and a potentially devastating one for Van Bronckhorst as far as his job prospects are concerned.
There are now as many points – seven – between Rangers and leaders Celtic as there are between the Ibrox side and Aberdeen in third. St Johnstone, meanwhile, move into the top six after their third successive victory and their first in the league over Rangers since March 2010.
The midday kick off might normally have been suggested as a reason for Rangers’ docile, one-paced performance. But they have been producing these displays at 3pm and in the evening in recent weeks.
The inquest will be long and painful. Much of it will centre on how Rangers managed to have so much possession, including 12 corners in the first half, and do so little with it. Fashion Sakala did hit the bar with a header.
Rangers seemed to run out of ideas long before half-time and were punished when Brown connected sweetly with the ball 25 yards from goal after Stevie May’s shot had rebounded off Ben Davies.
Alfredo Morelos and Scott Arfield replaced Davies and Malik Tillman on the hour mark, but it was St Johnstone who stretched their lead two minutes later. May easily beat Leon King near the byline and cut the ball back for Clark, who neatly clipped the ball in off the underside of the bar.
Tavernier’s strike after a half-cleared Barisic corner offered Rangers something to cling to. Their failure to build on this was instructive – as was their total of zero yellow cards.