Dustin Johnson, Freddie Jacobson and Tom Hoge are also tied for second at the four-round event in Texas.
England's Greg Owens and Ian Poulter are joint 28th on three under par.
Spieth dropped six shots in three holes as Danny Willett won the Masters in April, missing the cut at the Players Championship in his next outing.
The 22-year-old Texan, who won the US Open and the Masters last year, said: "I lost a little control with my iron play on some pretty easy shots that I will look to improve on but other than that I'm pretty pleased."
Spieth made his PGA Tour debut at the 2010 Byron Nelson, finishing tied for 16th aged 16.
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Jordan Spieth shot a six-under-par 64 to sit one behind joint first-round leaders Danny Lee, Sergio Garcia and Johnson Wagner at the Byron Nelson.