It means the Tigers remain second bottom, while Northampton are back at the Premiership summit with Bristol still to play on Sunday.
And Northampton soon lost another player as influential full-back Furbank was forced off for a head injury assessment.
Both teams failed to make anything stick during the opening 12 minutes, but Leicester were able to go in front thanks to a Ford penalty from in front of the posts.
Furbank was able to return to the field soon after as Northampton tried to exert some pressure.
And they did just that, using a scrum in the Tigers 22 to eventually allow Cobus Reinach to send Proctor through a non-existent Leicester defence.
Tigers were dealt another blow as wing Jonah Holmes was forced off with an injury, but the away side scored soon after as flanker Thompson got the ball down.
Ford kicked to make it 10-7, but the scores were soon level as Grayson landed a penalty earned by Alex Waller's rampaging run into the Tigers 22.
Saints then took the lead once more as fine combination play between Furbank and Hutchinson allowed Proctor to spin and score a second in the corner.
Grayson converted to a huge roar and Northampton were now firmly on top.
They scored again just before the break as Hutchinson released Proctor who ran a lovely line before giving the ball to man of the match Taqele Naiyaravoro for a trademark offload for the onrushing Ratuniyarawa.
Grayson converted again to make it 24-10, but Leicester responded after the restart. Ford landed a penalty after lock Alex Moon had been sin-binned for deliberately slapping the ball out of Leicester hands.
But it did not ruin Northampton's momentum and after Leicester's lineout woes continued, Reinach sent a long pass out to Collins, who bagged his team's bonus-point try.
Leicester were struggling to summon up any sort of response and there was still time for it to get worse as Dingwall, just on for Proctor, finished off another flowing move.
Grayson converted to make it 36-13 and Northampton continued to pile the pressure on until the final whistle, with Leicester left battered and bruised.