The 19-year-old Spieth and fellow American Castro finished their rounds on Friday and stood at seven-under-par 135 at Congressional Country Club in Bethesda, Maryland.
Argentina's Andres Romero, who had five holes to finish for the second round when the threat of lightning suspended play on Friday, made a late push to join them but bogeyed the par-five 16th on his way to a 66 and was one shot back on 136.
Tied at five-under 137 were big-hitting Belgian Nicolas Colsaerts (68) and South Korea's Lee Dong-hwan (66).
The cut came at three over par with Hunter Mahan among those failing to qualify for the third round. The former U.S. Ryder Cup player, who shot 72 for five-over 147, has been in the top 12 here four times, including a runner-up showing in 2009.
John Merrick aced the par-three seventh hole on Saturday with a six-iron from 178 yards but that was not enough for him to make the cut as he posted an even-par 71 for 147.
Castro and Spieth, a former University of Texas standout, are both seeking their first PGA Tour win, with Spieth competing on a sponsor's exemption this week.
(Reporting by Larry Fine in New York,; Editing by Gene Cherry)
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