The late score by the England full-back, who will play for Harlequins next season, guaranteed Northampton will stay at Franklin's Gardens for their semi-final on June 12.
Northampton's tries came from George Hendy, Rory Hutchinson, Tommy Freeman, Sam Graham, Furbank and Fin Smith, with England fly-half Smith adding three conversions.
Deian Gwynne, Ollie Thorley, Seb Atkinson, Max Llewellyn and Ben Loader scored Gloucester's tries, with Charlie Atkinson converting two and landing a penalty as well.
An entertaining first half ended all square at 19-19 and Gloucester were on course for victory when Atkinson kicked his penalty before Furbank had the final word.
But Northampton director of rugby Phil Dowson was frustrated by his side's error-strewn display.
"I'm a bit annoyed at the moment as we weren't at it today as there were loads of uncharacteristic errors and it didn't look as though we had the right mindset," he said.
"It was very hard work and Gloucester played well, but we weren't clinical or precise enough, but obviously I'm pleased to secure a home semi-final."
Saracens boss Mark McCall's final home game in charge ended in a 26-12 win over Harlequins that left his side on the verge of play-off qualification.
McCall, 58, is stepping down at the end of the season after 17 years at Saracens, 15 as director of rugby.
His time in charge has yielded six Prem titles and three European crowns. Another trophy remains a possibility, with next Saturday's clash against Exeter on the last day of the regular season a shoot-out for fourth place.
"It's never been about one person. It's never been about me, ever," said McCall.
This was Saracens' fifth successive win and former Ireland centre McCall added: "We're on this lovely run at the moment and every game presents a different kind of challenge."
Meanwhile, bottom-of-the-table Newcastle came from 35-10 behind at half-time to win 45-42 at home to Sale.
Alex Hearle sealed what was just Newcastle's second win in 17 Prem games this season when the centre went over in the closing seconds at Kingston Park to complete a hat-trick of tries.