The 20-year-old Spieth shot his third straight sub-par round, a 2-under 70 on Saturday that pulled him even with Watson.
The 36-hole leader stumbled a bit on moving day at Augusta National. After two rounds in the 60s and a three-shot lead at the midway point, Watson settled for a 74 that left him at 5 under.
Still, it was good enough to give him a share of the lead.
Matt Kuchar (68) and Jonas Blixt (71) were one shot back. Miguel Angel Jimenez shot the best round of the tournament, a 66 leaving him just two shots off the lead and tied with Ricky Fowler.