The 32-year-old teed off in Connecticut just four days after holding four-time major champion Phil Mickelson at bay during a tense final round at Merion.
The intervening period has been a whirlwind of media engagements, leaving Rose with little time to prepare and just keen to get the first round out of the way.
But he told www.pgatour.com: "The announcement on the first tee today, being announced as the 2013 US Open champion, I couldn't help but smile before I hit my first tee shot
"That's an achievement that I've been dreaming about."
Rose had more reason to smile as he birdied the first, but three bogeys in the next four holes left him two over par.
Rose then birdied the seventh and picked up four further shots in five holes from the 12th for a three-under-par 67, six shots back on first-round leader Charley Hoffman.
"I had a sluggish four or five holes where I struggled, but I stayed patient," Rose said. "I've stayed sort of committed to the same things that worked so well for me last week. That was my goal today, really.
"When you play a tournament like this, it's about keeping steady pace. If you put four rounds in the mid-60s together, you're going to be very, very close."