The eight points in the penultimate race of the season takes Force India to 120 points, 44 ahead of sixth placed Lotus going into the finale at Abu Dhabi.
Hulkenberg made the two-stop strategy work after starting from fifth on grid while his teammate Sergio Perez ended 13th, two spots lower than his grid position.
The Vijay Mallya-led squad have made history after an unprecedented year when it earned 19 points finishes and a third ever podium through Perez.
"My utmost satisfaction is we have improved performance steadily every year over the past eight years. I have a great team to whom I owe this," said Mallya, who is in talks with Aston Martin and Johnnie Walker to rebrand the team next season.
More From This Section
Perez and Hulkenberg will now be looking to hold on to ninth and 10th spot in the drivers' standings at the season finale in two weeks time.
"I am very happy with sixth place and with scoring the points that helped the team secure fifth place in the championship, which is great news. It is the best result in our history and shows the progress we have made over the years. This fifth place is a result of all the hard work from everybody in the team and we should feel very proud of what we have achieved together," said Hulkenberg.