Lee, 36, who had shared the overnight lead with Spaniard Rafael Cabrera-Bello, lifted his hopes of scooping the first European Tour victory of his career by firing a three-under-par 69 for a 12-under total of 204.
Mickelson surged into contention with a dazzling 63, taking the world No 5 into a tie for second on 206 along with India's Gaganjeet Bhullar (66). A further stroke adrift were Rory McIlroy (70), who was hindered by a two-shot penalty, and Spain's Pablo Larrazabal (68).
Early starter Mickelson charged through the field with a dynamic round containing nine birdies, one eagle and two dropped shots. The five-times Major winner conjured up a four at the par-5 18th after finding a bunker off the tee and sandy waste with his second shot.
With a palm tree in front of him, the 43-year-old Californian produced a low, fading escape with his third, which scuttled up on to the green - and he punched the air in delight when he rolled in his putt from 30 feet for his closing birdie.
"It probably wasn't very sensible of me to try to go for the green but hey, that's what I do," Mickelson said.
"I was fortunate in that I just had enough room to trap out a low pitching wedge that flew under the leaves and up on to the green. Bones [caddie Jim Mackay] did not like the decision and I don't blame him. It probably wasn't my smartest play."
Lee will line up alongside the left-hander in the final group today and said he would take heart from the victory of another unheralded player, Welshman Jamie Donaldson, in Abu Dhabi 12 months ago.
"You can look back on that and say fairytales do happen," said the Stirling-based player, whose best finish on the Tour came when he lost a play-off to Thomas Bjorn for the Omega European Masters last September.
"The quality of the players behind me is nothing I have been used to before. I can't control what they are going to do, I just have to play the best I can.
"My career is starting to gradually get better and better and steadier and steadier which is probably the most important part. To come out on top tomorrow would be a joyful occasion."
A clearly angered McIlroy incurred a two-stroke penalty after breaching the rules while taking a drop at the second. The Northern Irishman initially thought he had carded a 68 to finish 11 under par and just one shot behind Lee, only to be told of a possible infraction by Dave Renwick, caddie to his playing partner Ricardo Gonzalez.
Renwick felt McIlroy had not taken full relief from a spectator crossing on the second hole and after a review, European Tour chief referee John Paramor applied the penalty.
"There are a lot of stupid rules in golf and this is one of them," said the former world No 1. "It's unfortunate. If anything it was a disadvantage because I dropped it in a bad lie and did not make birdie.
"I guess I just have to try to make up those shots as early as possible tomorrow and try to get off to a fast start."