Leeds trailed 18-13 as the Guinness Premiership relegation showdown crept into time added on but a try from substitute scrum-half Danny Care levelled the score.
Gordon Ross missed the routine conversion and Saints still had time to stage one last attack, winning the penalty which Reihana converted.
With fellow strugglers Bath beating Wasps earlier in the afternoon, victory became even more crucial and it was Saints who held their nerve.
Scotland winger Sean Lamont, back after recovering from an ankle injury, and Jon Clarke crossed while the boots of Reihana and Carlos Spencer did the rest.
Leeds struggled to match last weekend’s rampaging 48-3 Heineken Cup win over Cardiff but their resilience in the second half – which Saints dominated for lengthy spells – kept them in the hunt until the end.
England Under-21 winger Tom Biggs underlined his finishing skills with a brace of tries in a bonus-point defeat which cast the Tykes nine adrift at the foot of the Premiership.
Northampton made an impressive start and took full advantage of a charged down kick from Justin Marshall by cranking up the pressure on Leeds’ line.
Jon Clarke sliced open the Tykes’ defence with a robust run before finding Bruce Reihana but the Kiwi’s pass to Ben Cohen was intercepted.
Saints could not be contained for much longer and the visitors cracked in the seventh minute with a sublime chip from the outside of Spencer’s boot finding Lamont who raced home.
But Leeds were back on level terms when Tom Biggs won the sprint for Roland De Marigny’s grubber, touching down in the corner. Both conversions hit the post.
Former Springbok winger Andre Snyman broke several tackles in the 28th minute to carry Leeds deep into opposition territory and when Saints infringed, Gordon Ross kicked the penalty.
A magnificent solo try from Biggs extended the Tykes’ lead with the 21-year-old winger capitalising on good approach work from Rob Vickerman and weaving his way over.
Northampton finished the half with a flourish with Reihana nearly wriggling through a packed midfield, but they were more successful moments before the interval.
Powerful running from David Quinlan opened up a hole in Leeds’ defence and the Ireland centre slipped a pass out of the tackle to Reihana who dashed in underthe posts before converting his own try.
Cohen lit up the start of the second half with a 30-yard break from his own half but the England winger was then forced off after sustaining a cut under his right eye in an incident involving Marshall.
Marshall was trying to escape from the base of a ruck but Cohen was pulling him back, so the former All Black scrum-half threw a punch which earnt him 10 minutes in the sin-bin.
Leeds’ line came under increasing pressure with lock Damien Browne help up over the line and the alert Ross saving a pushover try by diving on the ball just as Saints’ scrum crossed the line.
Cohen returned to the action as a long-range Spencer penalty increased Northampton’s lead to five points.
Leeds were not finished yet, however, with waves of attacks creating big holes in Northampton’s defence which substitute scrum-half Care punished four minutes into injury time by darting over from close range.
Ross missed the conversion which would have put Leeds ahead but it did not matter anyway as Reihana still had time to clinch victory with his penalty in the 88th minute.