Saints' triumph has restored their lead over the Tayside outfit to four points and also put a full-stop on a disastrous six-game losing run that had transformed the Paisley men from SPL top six residents to relegation battlers.
But now Teale wants the Buddies to travel to Ross County tomorrow night and build on this impressive victory to get back in among the pack.
The Saints star said: "It is hard to say just how important this win will be but given the run we have been on it was absolutely vital we got it.
"I don't think our performances have merited a six-game losing run but that is the way it has panned out and maybe we got that wee break we needed against Dundee we have been missing of late.
"What is absolutely vital is that we build on it at Ross County tomorrow. We have given ourselves the perfect platform into the trip up the road and it is vital that we do not waste it."
There were a number of big performances in the Paisley ranks with two-goal Stevie Thompson outstanding and teenage debutant John McGinn also impressive.
Teale was right up there with a string of fine deliveries and a willingness to work at either end of the park. Now the former Scotland star believes his side have even more to give.
Teale said: "It is all about hard work now. We have got to be making sure we work harder than the opposition every time and must do so again in Dingwall tomorrow.
"But it is great to see young lads like John McGinn coming in and showing up so well.
"For me that is all very positive for St Mirren."
As might be expected with so much riding on it, this encounter quickly developed into a full- blooded affair but with matters even a moment of incendiary madness left Dundee with a numerical deficit.
Colin Nish showed his studs in a wayward challenge on Paul Dummett in 27 minutes and referee Willie Collum flourished his red card with some relish.
Four minutes later the hosts made their advantage count as Lewis Guy rounded Rab Douglas before attempting to slot the ball home, only for it to be cleared off the line where Stevie Thompson was lurking to put his side a goal up.
Right on the stroke of half-time McGinn's cheeky chip was brilliantly tipped onto the roof of the net by Douglas as the veteran keeper once again demonstrated a dexterity that mocked his advancing years.
After 64 minutes the visitors found a way back when Goodwin handled in the box to allow Ryan Conroy to equalise form the spot, but when Teale's free-kick was headed in by Thompson St Mirren's lead was restored within 10 minutes.
Four minutes before full-time Dougie Imrie smashed home his first goal for the Paisley men to finally secure the win.