The 38-year-old from Bathgate signed for his lowest round of 10-under par 62 – two days after matching his previous best of 63 – after firing in his second eagle of the day, and fourth of the week, with a 40-yard bunker shot at the last.
Gallacher had earlier taken just three shots at the par-5 13th, after almost claiming an albatross. From a massive drive he needed just an 8-iron and it hit the flagstick before stopping less than four feet away.
The former Scottish and European amateur champion had earlier sent his third shot at the par-5 13th into the hole via the flagstick on his way to beating Woods' tally by one. He now stands on the brink of adding a second European Tour success to his only previous win, at the Alfred Dunhill Links Championship in 2004.
Told he had outdone Woods, Gallacher merely said: "It's nice to get one over Tiger but it's all about finishing in front tomorrow. That's all that matters."
One of the first to shake Gallacher's hand after his round was fellow Scot Chris Doak, who goes into the last day of his first Dubai event sharing 10th place on 11 under par.
Doak had been tied for fifth overnight but spoiled any forward momentum with a double bogey at the seventh in scoring a one-under-par 71.
In overcast and rainy conditions, Gallacher, the nephew of the former Ryder Cup captain Bernard Gallacher, ran up three birdies in his first five holes.
He added further birdies at the 11th and 12th before eagling the 13th with his 8-iron approach shot. At the last, Gallacher stood in the middle of the fairway 232 yards from the flag and already at eight under for his round but with a lump of mud on his ball.
He said: "It was a perfect rescue club distance but I couldn't chance it with mud on the ball, so I thought I would hit a 3-wood into the bunker. If I had flushed the 3-wood it would have ended up in someone's dinner in the corporate enclosure or landed short in the water. But the bunker shot came out perfectly and went straight into the hole."
He added: "I'm excited and looking forward to tomorrow. I'm pretty familiar with this course – I come out here on holiday with the family."
Gallacher has contested 205 Tour events since defeating Graeme McDowell in a play-off over the Old Course at St Andrews in the Dunhill Links Championship nearly eight and a half years ago.
In that time he has had three second-place finishes, one of them behind Lee Westwood in Dubai a year ago. Gallacher has also been in the top 10 on 22 other occasions and banked more than £4 million in prize money.
However, four years ago he had to return to the Tour qualifying school during a battle with the rare disease sarcoidosis, which affected his lungs and joints.
If successful today, Gallacher will become the second Scottish winner in the Tour's first six events of the season, after Scott Jamieson's victory at the Nelson Mandela Championship in South Africa in December.
He would be almost certain to qualify for a debut appearance at the WGC-Accenture Matchplay Championship in Arizona, which tees off on February 20, and would rise from 111th in the world rankings to inside the top 60 for the first time.