Hurley, a U.S. Naval Academy graduate who calls nearby Annapolis his home, fired a six-under 65 to join playing partner Rahm on 11-under-par 131 at Congressional.
Alone in third place was 53-year-old Vijay Singh of Fiji, whose five-under 66 took him to eight-under at the halfway mark.
Lurking another shot back was Ernie Els, tied with three others at seven-under on the course where the big South African won his second U.S. Open crown in 1997.
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Rahm was delighted that he was able to register another strong score in his second professional round after opening with a 64.
"I couldn't be happier," the 21-year-old from Barrika said. "(Thursday) was a great round and after a great round usually it's hard to follow it. I'm really proud of myself."
Three-times major champion Singh, who has not won on the PGA Tour since 2008, could become the circuit's oldest winner with a victory.
Hurley, looking for a first PGA Tour victory, credited his impressive start to his play on the greens.
"I made a lot of good putts today but they were all really tricky," said Hurley, who was encouraged by fans shouting out "21412" as he confidently made his way around Congressional.
"21412 is the zip code of the post office on the Naval Academy," Hurley explained.
Tied with Els on seven-under were Americans Webb Simpson, the 2012 U.S. Open champion, Bill Haas and Harold Varnell III.
(Reporting by Larry Fine in New York; Editing by John O'Brien)
