Stroud shot a 6-under 64 early in the day, a score that was matched late in the afternoon by Ross Fisher.
This is the final event of the regular tour season and the last chance for players to earn a place in the 125-man field for the FedEx Cup playoffs. In addition, the leading 125 money winners at the conclusion of this tournament will be fully exempt for next year's circuit.
Fisher could be a major beneficiary this week since he began the tournament in 162nd place on the points list. A win would vault him into 56th place.
Stroud is assured a playoff spot since he is 50th on the points list. He has already won more than $1 million this season thanks to four Top 10 finishes, including a career-best second-place finish at the Travelers Championship in June.
Spieth is seeking his second victory in a month, having won the John Deere Classic prior to his 19th birthday.
His round was highlighted by his second shot to the par-5 15th, an effort that sailed over the green, slammed into the metal grandstand, bounced back all the way across the putting surface and rolled off the front edge. He then chipped within six feet and made the putt for an unlikely birdie.
Swim Week Miami Beach 2014 [PHOTOS]