Haas and Driscoll put up matching rounds of 3-under 68 while Castro chipped out from 26 yards on the final hole to save par and finish with an even-par 71.
Romero posted a 1-under 70, joining the other three atop of the leaderboard at 7-under-par 206 at Congressional Country Club's Blue Course.
Alone in fifth place at minus-6 was Jason Kokrak, who also posted a 70.
Charlie Wi (65) and Tom Gillis (66) ended Saturday knotted for sixth one stroke further back.
Tied for eighth at 4-under 209 were Brandt Snedeker (69), Brendon Todd (68) and 19-year-old Jordan Spieth (74), who came into the day tied with Castro for the lead.