The Australian trailed overnight leader Phachara by a shot after Friday's play but hit six birdies around the composite course to pull level with 18 holes remaining.
The pair will be looking to join a winners list that includes former major champions Rory McIlroy, Greg Norman and Justin Rose when the tournament, being played for the first time in four years due to the COVID-19 pandemic, concludes on Sunday.
In overcast and breezy conditions, the 2022 British Open winner made a steady start to his day, picking up a single shot in his first seven holes.
But back-to-back birdies at the eighth and ninth ignited his round and he looked set to dominate.
Smith drained a 30-foot putt at the 15th to go into sole possession of the lead but at the next dragged his tee shot into the trees and, after only just managing to play his second out of the bushes, the Australian escaped with a bogey.
Phachara's birdie at the same hole saw the lead change hands between the playing partners, but Smith responded by rolling in a birdie putt from eight feet at the 17th to quickly make up for his error and pull level with the Thai.
Twelve players lie within five shots of the lead duo, including former US Open winner Graeme McDowell, with the Northern Irishman on 12-under, four strokes adrift.
