Stenson is looking to become the first man to win the Race to Dubai and FedEx Cup in the same season and is in contention to clinch them both in the same imperious fashion.
He went into the Tour Championship in September as one of five players who could win the FedEx Cup by winning the tournament and led from start to finish to claim the 10 million dollar bonus.
This week the Swede was one of three players in similar control of their own destiny and shares the lead going into the final round of the DP World Tour Championship in Dubai.
Stenson carded a third round of 67 to finish 17 under par at Jumeirah Golf Estates, one shot ahead of France's Victor Dubuisson who fired 11 birdies - one short of the European Tour record - in his 64.
Justin Rose and Graeme McDowell can still deny Stenson the title with victory here, with Rose 11 under and McDowell eight under after both shot rounds of 68.
A win for Poulter would leave Stenson needing to finish second to claim the Harry Vardon trophy, with Poulter four behind on 13 under following a 66.
"I caught him today and I'll catch him tomorrow, it's whether or not I can keep hold of him," said Poulter, who briefly drew level with Stenson before the Swede - a neighbour along with Rose and McDowell in Lake Nona in Florida - birdied four of the last five holes.
"I'm pushing really hard on this course and it's easy to make mistakes when you are doing that. I made two bogeys on par threes which is frustrating but I am right in there and I can't ask any more than that."
Poulter has the added motivation of a 100 dollar bet with Stenson, at 10/1, that he will overtake him, with the loser having to act as the winner's personal waiter on a night out as well.
"The odds would be significantly shorter now and I have put myself in position to try to kick his backside tomorrow," Poulter added. "It's fun hunting Henrik and if I can get off to a decent start it's going to be great on the back nine.
"Being European number one would be a huge highlight in my career."
Stenson does not have to win on Sunday to become the second Swedish player after World Cup-winning partner Robert Karlsson to top the money list, but he does not want to think about all the different permutations.
"I am trying to avoid all that," the 37-year-old said. "I know I can win the Race to Dubai even if I don't win here, but why not try my hardest to win this tournament? If I do I know that both trophies are coming home with me.
"It's a great achievement to be the one who wins the most money throughout the year and I would love to emulate Robert. The guys are going to try their best to attack but if anything it makes me try even harder.
"They are the ones that need to overtake me so I am trying to stick to my game plan. It's working so far so I don't see any point changing."
Dubuisson is seeking back-to-back wins following his maiden European Tour victory in the Turkish Airlines Open on Sunday, but the 23-year-old would need Stenson to finish outside the top 30 to also win the Race to Dubai.
McDowell was just five behind Stenson when he completed his round and insisted he was still "alive and kicking", but added: "Hats off to Henrik, he came here this week and is doing exactly what he needs to do.
"He has been the best player in the world the last six months and he needs to slip up tomorrow and I need to mount a massive challenge.
"I have not done much better than 68 round here before and I will need to do so tomorrow. I have not played my best the last three rounds but I am proud of how I have hung tough."
Three former world number ones are inside the top 10 on the leaderboard, with Lee Westwood 11 under and Luke Donald and Rory McIlroy 10 under.
Westwood was seven under for his first 11 holes but bogeyed the 12th and was able to find just one more birdie after that, although he did save par on the 18th after driving into the water.
"I got in my own way a little bit around the back nine there," Westwood said. "It's a good 65 but seven under through 11, you're looking for a few less than that.
"My swing hasn't been in sync all year, I'm sort of fumbling my way around the golf course and it's something I'm going to work on over the winter."
Donald returned a 67 that featured birdies on the last four holes, while McIlroy - who followed in Donald's footsteps by winning the money list on both sides of the Atlantic in 2012 - came home in 32 in his 68.