Newcastle had more of the ball and more shots on goal but trailed to Rúben Neves' crisp strike going into stoppage time.
But then, from nowhere, Saint-Maximin sent a glorious 20-yard volley flying past José Sá to deny the home side what would have been their first win of the season.
With new signing Alexander Isak ineligible and Callum Wilson and Bruno Guimarães injured, Sean Longstaff made his 100th appearance for his boyhood club while Chris Wood started after scoring at Tranmere in midweek.
The first chance of the game fell to Wood in the fourth minute, when Joelinton slid in to prod the ball though to the New Zealand international, but he was forced wide by Sá and saw his shot blocked by the goalkeeper.
Three minutes later, great work on the right from Goncalo Guedes presented Pedro Neto with an opportunity, but he prodded over with the ball dropping onto the roof of the net.
Newcastle felt they should have been awarded a spot-kick in the 12th minute as Longstaff clearly had his shirt pulled in the box, but play continued and Joe Willock eventually stabbed wide. Then soon afterwards, Longstaff had a powerful effort blocked by Neves.
The home side withstood some sustained United pressure before beginning to threaten themselves, with Matheus Nunes sending a free header horribly off target before Jiminez twice came close.
But in the 40th minute, Wolves took the lead through Neves. Bruno Lage's side worked the ball from right to left before Guedes teed up the Wanderers captain, who drilled home from 22 yards.
And United couldn't respond before the break, although Saint-Maximin saw a low shot comfortably fielded by Sá after cutting inside from the left.
They continued to look for a leveller after the restart, with Miguel Almirón's cross from the left almost put through his own net by Nathan Collins, who was relieved to see the ball flash just wide, then Willock setting up Fabian Schär for a low shot from distance which took a touch on its way past the post.
Wolves still posed occasional questions of their own, with Pope saving comfortably from Neto just before the hour mark and again from Nunes in the 80th minute, while Jiminez had a goal rightly disallowed for a shove by Neto on Ryan Fraser in the build up, but were largely content to try to hang onto their advantage throughout the second period.
And despite the introduction of Fraser and Matt Targett, then Elliot Anderson and Jacob Murphy in two attack-minded double changes, it looked like they would do exactly that.
But then came Saint-Maximin's stunner - and the Frenchman, who had moved to a central role in the second half, was then denied a dramatic winner by Sá in stoppage time after a swift Magpies break, before Anderon sent a header crashing against the bar in the dying seconds.
