This all depends on Inverness lifting the Scottish Cup next weekend, which would allow Saints to take up their position in the Europa League after finishing the season fourth in the Scottish Premiership table.
But Sunday’s match in Aberdeen took time to get going, with not a single effort on goal registered during the opening 25 minutes.
Thankfully, this dire spell was broken by St Johnstone’s Michael O’Halloran, whose shot flew into the side netting.
The game duly opened up during the remainder of the first half. Saints keeper Alan Mannus did well to touch a Jonny Hayes shot on to a post and also denied Cameron Smith while, at the other end, Liam Caddis and Chris Millar went close from outside the box.
After the break, the match remained end to end until the deadlock was finally broken 20 minutes from time.
Less than a minute after coming on to the field, Kane collected Tam Scobbie’s assist before out-sprinting the home defence and drilling his shot past keeper Scott Brown.
As second placed Dons chased an equaliser, Joe Shaughnessy forced a good save out of Mannus who tipped his 22-yard effort over the bar.
Shortly afterwards, a six-yard header by Ash Taylor flew narrowly wide of the left post but Saints held on to keep alive their chances of playing in Europe next season.
Their hopes now rest on Inverness winning next Saturday’s showdown at Hampden Park where Championship side Falkirk will hope to create a massive shock and which would also leave Saints massively disappointed.