Birmingham had hauled themselves level 13 minutes from time through a Paul Devlin penalty and looked good for the draw before Poyet blasted a left-foot volley past Andy Marriott in the 88th minute.
It was a crushing blow for Birmingham and for Marriott in particular who earlier handed Tottenham the lead in farcical circumstances with only seven minutes on the clock.
The goalkeeper was making his debut after signing from Barnsley two weeks ago and could not have imagined a worse start to his Birmingham career as he failed to check behind him before rolling the ball out and watched in horror as Robbie Keane ran round the back of him to tap the ball into the empty net.
It was a sickening blow for Steve Bruce's side especially as they could already have been in the lead after Geoff Horsfield dragged a shot wide from just six yards with only two minutes gone.
Going behind seemed to stun the visitors for a while and they could have been further behind within 20 minutes as Poyet had a header cleared off the line and Darren Anderton shot narrowly wide.
However, City regained their composure and began creating goal opportunities with Horsfield volleying just over and Christophe Dugarry seeing his shot turned round the post by Kasey Keller.
As the visitors turned up the pressure they had three appeals for a penalty turned down by David Ellery before half time.
All three decisions seemed spot on and there could be no arguing with the referee when he finally pointed to the spot in the 77th minute.
Stan Lazaridis pumped a hopeful ball into the area and Dugarry went down under a clumsy challenge from Poyet.
Devlin made no mistake from the spot drilling his shot straight down the middle and it looked like Birmingham would go home with a point only for Poyet to make his dramatic intervention.
A long kick from Keller seemed to evade everyone before reaching the Uruguayan on the left-hand edge of the area and he instantly smashed the bouncing ball past Marriott and into the far corner for the winning goal.