World number three Stenson, England's Justin Rose and Northern Ireland's Graeme McDowell can clinch the Race to Dubai, formerly the European Order of Merit, with victory in the season finale.
The Swede - the Race to Dubai leader - sunk three birdies in the opening seven holes and was steady on the back nine before three-putting on the final hole at the Greg Norman-designed Earth course.
"I'm playing nicely and I just let my focus slip on the last - I'm tired and it's hard work out there," Stenson, 37, told reporters. "I hit a lot of fairways and some nice approach shots into the green, it's just tough to read them - everyone had a few chances that went by.
"All the guys are running on fumes - probably a quarter of the field is battling injuries at this point of the season."
Rose admitted he was not at his best as the U.S. Open champion finished two-under 70 in a solid, if unspectacular, round that saw him drop his first shot of the day on the 17th.
"I mishit a lot of shots today - they weren't really getting me into trouble, but I wasn't firing on all cylinders," said Rose. "Patience is a big part of it so at no point today was I worried about where Henrik was."
McDowell has never made the top-10 in Dubai and he started poorly to be three-over with five holes to play.
But the world number 11 sunk a short birdie on the 14th, clawed back another shot on the 15th with a 15-footer and claimed a third birdie in successive holes on the 16th with a 25-foot putt for round of 72.
"That was key to getting back into the middle of the pack," said McDowell. "I could have shot myself out of it. It's very much a case of not letting this golf course get to me too early in the week. I've let these greens get in my head in the past."
England's Ian Poulter and Welshman Jamie Donaldson, who can also win the money list should they prevail in Dubai and Stenson finishes third or lower, scored 69 and 68 respectively.
"Every time I had a putt it was a slippery little put," said Poulter. "Downhill, left-to-right, right-to-left - really awkward and the greens are quick so it's hard to hit it as firm as you want to because if it misses it's going five feet past.
"They're tricky to read so I'm walking away frustrated from today's round but happy to be only three behind."
The day belonged to Spain's Canizares. The world number 184 matched McDowell's birdie run from 14 to 16 and dropped just one shot all round to card 66.
Thailand's Kiradech Aphibarnrat and Australia's Marcus Fraser are one behind on 65 and would have been tied for the lead had they both not dropped shots on the 620-yard 18th.
Former world number one Rory McIlroy, seeking a first win of 2013, sank birdies in three of the opening four holes on a cloudless morning as girlfriend Caroline Wozniacki looked on.
But bogeys on the fifth and eighth holes stymied McIlroy's charge, and although the defending Dubai champion birdied the seventh he dropped another shot after finding the water on the 18th to end on 71.
(Reporting by Matt Smith; editing by Justin Palmer)
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