The Welsh side declared on 311 for five before lunch on the final day of a game they had been in control of for the majority of, setting the County an improbable looking 355 to win from a minimum of 79 overs.
But thanks to remarkable knocks from Vasconcelos, who hit a career-best 185 not out from 221 balls, and Keogh, who made 126 from 140 balls, Northants breezed to their target with seven wickets and more than six overs to spare.
The Glamorgan bowlers had no answers to the onslaught, as the County made the most of a flat pitch, a fast outfield and a short boundary on one side to cruise along at four and a half runs per over.
No visiting bowler managed to keep their economy rate below 4.4 runs per over, with four of the seven used going at more than five.
And Vasconcelos, who also scored a century in the County's opening draw with Kent, said that once Glamorgan had set the target, he and his team-mates were pretty confident they could prevail.
“From the moment they declared we had a sit-down and said that we were going to be positive and take it hour-by-hour and session-by-session," said the opening batsman.
"We always knew we’d have a chance if we didn’t get bowled out with the batting we have."
Vasconcelos and Ben Curran (24) set the early tempo, putting on 81 in 17 overs, and even the loss of Curran and Charlie Thurston for a duck in the space of eight balls didn't knock Northants off their stride.
That brought Keogh to the crease, and the pair proceeded to hammer a partnership of 239 to leave the County on the brink of their brilliant victory, before Luke Procter joined Vasconcelos to complete the job.
“Me and Rob feed off each other quite nicely. We are right-left hand which gives us a few bad balls," said Vasconcelos
"We know each other quite well, and used to live together.
“We play our best cricket when we show a bit of fight. We showed that against Lancashire (when the County got to within 13 overs of an unlikely draw) and again in this game.
"We are never out of it and we always believe we can win the game.”
Keogh also scored his second century of the season, and his 11th first-class ton in Northants colours, and he said he was able to play with freedom as he knew he had the backing of the rest of the squad to do so.
“The boys up top got us off to a flier so for me it was about being positive and going early so I didn’t put too much pressure on Ricardo," said the 29-year-old.
“He was flowing so nicely I just tried to get ticking and rotating the strike.
“We had the backing from the whole squad before we went out there that we were going to chase it down so there wasn’t really any doubt in our mind.”
The win saw Northants jump up to fourth in the LV= Insurance County Championship Group 3 table, and within 13 points of Yorkshire in second place.
In the other matches, Yorkshire were 48-run winners over Sussex, while leaders Lancashire thrashed Kent by an innings and five runs.
Northants are back in action on Thursday when they travel to Headingley to take on Yorkshire.