England duo Mark Regan and David Rees were sin-binned late in the game and the Saints duly punished the home side with two tries but Leeds held out desperately for the win.
Four members of Andy Robinson's England squad for next week's game against Canada at Twickenham were determined to impress, with hookers Regan and Steve Thompson enjoying a tremendous tussle.
Leeds' winger Iain Balshaw and Northampton counterpart Ben Cohen were also looking to boost their prospects of facing the Canadians though they had few opportunities to show their skills.
Northampton, who destroyed Llanelli in the Heineken Cup last week, arrived at Headingley with a miserable run of five Premiership defeats behind them, while Leeds coach Phil Davies demanded a big improvement on his side's inept display in the European Challenge Cup defeat against Grenoble.
Leeds took a seventh minute lead when Gordon Ross landed a towering long range penalty from near the right touchline, but Northampton's forwards took them close, fullback Bruce Reihana was held just short and when Leeds were penalised near the posts Paul Grayson levelled the scores.
The kicking of Tim Stimpson often gained Leeds relief but Northampton had a let-off when Ross and Chris Bell put scrum half Alan Dickens through but he hesitated and was caught when he should have scored.
Instead the Tykes had to be content with Ross' second penalty to restore the lead, but again the Saints hit back quickly through Grayson's reliable boot.
Leeds led 9-6 at the break, Ross kicking his third penalty in stoppage time of the first half when Saints' flanker Andrew Blowers was sin-binned.
Leeds made a storming start to the second half with 14 points in nine minutes. With Blowers still in the bin, Regan forced his way over by the posts for the first try, Ross landing the conversion.
Then good work in the forwards created the position for Snyman to send Bell over the line, Ross kicking his fifth goal from as many attempts.
Regan was sent to the bin on 63 minutes and Leeds were down to 13 men when Rees followed him five minutes later.
Northampton cashed in, prop Chris Budgen scoring wide out and Grayson converting.
Saints captain Corné Krige then went in on the overlap but Grayson's kick struck an upright and stayed out before he kicked a late penalty to gain the all-important bonus point.
For Leeds Tykes:Tries: Bell, ReganCons: Ross 2Pens: Ross 4
For Northampton Saints:Tries: Budgen, Krige Con: Grayson Pens: Grayson 3