The 27-year-old birdied the 18th hole as he completed a solid opening 69, but not before two young spectators made off with his golf ball after a pulled tee shot into the rough.
Laughing off the incident, Rahm said: "I'm pretty sure I know who it was. I recognised the two kids that were running the opposite way with a smile on their face. I am 100 per cent sure I saw the two kids that stole it."
After introducing a new ball into play, the current world number two was given a free drop away from an immovable obstruction and went on to complete a birdie.
"I'm just really happy somebody spotted the ball first," added the Ryder Cup star. "We knew exactly where it was.
"After the free relief I had 135 yards to the pin, in an area where the rough wasn't that thick. I don't think they expected anybody to hit it there or be around there, so I was able to drop it in an area that was a little downgrain."
After his birdie putt, the Spaniard was clearly enthralled and produced a fist pump reminiscent of his reaction to last year's US Open triumph at Torrey Pines.
Despite this, the player played down that notion, saying: "It's not really comparable. It's just more of a thank-God-I-made-a-putt-type deal. I feel like I played pretty good golf all day.
"I just saw a lot of putts get close and not go in, and to hit two wayward drives in the last two holes and somehow end up with two birdie putts and making the last one to break par on the first round of the US Open, it's quite a big deal."