Northampton bossed the close exchanges and a penalty try plus further scores from Lee Dickson and Dylan Hartley - as well as four points from Stephen Myler's boot - gave them a 19-16 half-time lead.
Wasps had twice been reduced to 14 men as Rhys Thomas and Tom Palmer went to the bin in the first half, but Tom Varndell's try, two penalties and a conversion from Stephen Jones, and a three-pointer from Elliot Daly kept them in it.
And centre Daly's wonderful finish down the left, after another Jones penalty, briefly put them on course for a remarkable victory.
But there was still time for Ashley Johnson to become the third Wasp to receive a yellow card, and another punishing series of Saints drives ended with Day getting the crucial fourth try at the death, with Myler's conversion sealing the win.
Northampton's renowned forward power was clear for all to see from the off as they made light of the freezing conditions.
Their first driving line-out put the Wasps pack in reverse and when hooker Thomas pulled the maul down referee David Rose had no hesitation in awarding a penalty try and sending the Wales international to the bin.
Another monstrous drive of almost 40 metres put Wasps under the cosh again seconds later, although the hosts escaped to get on the scoreboard with a long-range penalty from Daly.
But Northampton's might told again in the 16th minute, Wasps once more tried to collapse and prevent the inevitable, but scrum-half Dickson wormed his way over anyway.
Myler missed the conversion and Wasps replied instantly with a wonderful finish from Varndell from their first attacking chance.
Billy Vunipola's pass had left his wing with plenty to do, but Varndell turned on the afterburners to evade James Wilson and race in from halfway.
Jones added the extras and soon slotted a penalty to give Wasps a remarkable 13-12 lead considering the difficulties they were experiencing at close quarters.
Normal service was soon resumed as Palmer, back after a three month injury lay-off became the second Wasp in the bin for bringing down a Saints maul.
The visitors punished the ill-discipline as Hartley crashed over and Myler converted.
Jones' second penalty ensured Wasps were just three adrift at the break although there was little alteration to the pattern of the game in the third quarter.
Time and again Northampton easily made yards through their pack, but, as in the first half, they turned down several kickable penalties in an effort to kill Wasps off with a try.
Wasps grew in belief when Hartley threw in crooked at a close-range line-out on the hour and Wasps, now with England stars Joe Launchbury and James Haskell on the field, rampaged up field to earn a penalty which Jones slotted to tie the scores.
From a position of complete dominance, the visitors were rocking, and Wasps punished them with a well worked try in the 62nd minute.
Replacement hooker Tom Lindsay charged through several weak tackles before Johnson freed Daly out wide.
The centre shrugged off Myler and beat a feeble Ben Foden tackle to dot down in the corner as Saints protested for a foot in touch.
But television match official Graham Hughes ruled in the affirmative and the try was given.
Saints desperately sought a response, and Johnson became the third Wasp to receive a yellow card for illegally stopping a Northampton drive, leaving them helpless to prevent Day snatching the win and a bonus point.