The 36-year-old Tinning, who will retire after 15 years on the tour, was two shots back at the halfway mark. She made four birdies en route to a 3-under 69 to pass overnight leader Lydia Hall of England.
Reid shot a 68, earning a share of the lead on the final hole at the season-ending tournament in Dubai.
Hall (72) remained a shot back after she recovered from an early double bogey. She was tied with Sweden’s Anna Nordqvist (71), who briefly topped the leaderboard before falling back after a late bogey.
Michelle Wie, battling a bad back, had a roller-coaster round of 73. She birdied the third hole, but had two bogeys on the back nine before stringing together two birdies. She double-bogeyed the 18th to tie for 17th.
Tinning hasn’t won on the tour since a 2005 victory in Denmark. She went for the pins and made several clutch putts, including one on 15 to save par and on 16 for a birdie.
“This morning when I went out to play, I was really nervous the first few holes,” she said. “And it was funny. I said to my husband ‘Well, this is actually what I’m going to miss’. So I’ve got to enjoy it, even though it was a bit terrifying.”
Reid, who won her first tournament in Turkey this year, moved into contention after making three birdies on the front nine. She finished with two more birdies on the final two holes.
“Yeah, it would be a nice little Christmas present, wouldn’t it, to win this week,” said the 67th-ranked Reid.
Wie, who went to the practice putting green after her round, lamented some missed opportunities on the front nine. The normally big-hitting Wie had two bogeys and a double bogey on the par 5s on the back nine.
“I didn’t play well on the par 5 in the end. Oh well,” Wie said of the 18th hole. “I didn’t make any birdie putts in the beginning, which is a struggle for me. Other than that, I played pretty solid. I just have to monkey with a couple of shots.”
On Thursday, Wie admitted she was playing in “survival mode” because of ongoing back problems. She said she expects to be fit for next season.
Wie was limping slightly this week at the Emirates Golf Club because of the injury. She is getting physical therapy and seeing a chiropractor for the back problem that sidelined her the past few weeks. Wie withdrew from the Lorena Ochoa Invitational last month.