The 56 year is at 5 under and tied with Tom Watson and Jeff Maggert as the event enters the weekend.
Fowler, who has won his last two events on the European Senior Tour, took advantage of an early tee time on day two and added a second round of 66 on the demanding layout.
"I've been really happy with my game, said Fowler after his round. "Best I've putted for 20 years. I've got a new putter, and it's nicely balanced, and it's suited me. Yeah, my good golf started when I qualified for the Senior U.S. Open in Kansas a month ago. It's carried on.
"I don't think anybody is going to go super low here. There's not many par 5s. There's only one reachable par 5, and that's the 1st hole. It's a tough golf course. The greens are firm and fast. So if you're out of position, it's very difficult to get it close. I don't think anybody will run away, which I suppose is a normal U.S. Open. Just got to keep playing nice, solid golf, and going to try and stay cool."
Peter Senior is just three shots from the lead after his second consecutive round of 69.
Want video tips delivered straight to your inbox? Subscribe to iseekgolf.com newsletters.