A strong end to Saturday's session, when carding five birdies in the last seven holes, was enough to see Rose join Garcia at the summit on six-under.
Thomas Pieters, Charley Hoffman and Rickie Fowler all relinquished their overnight lead, though the latter finished just a shot further back on one-under for the day and remains in strong contention ahead of the final round.
It proved to be a good day for former winner Jordan Spieth, too, as he dropped just one shot to climb from a share of 10th into fourth, joint with Hoffmann and Ryan Moore.
Elsewhere, Lee Westwood is tied for ninth on 68 for the tournament and Rory McIlroy is three shots further back on level par in 11th.
Four former Major winners make up the top 10, including 2013 US Open champion Rose.