Vijay Singh and Spike McRoy share fourth place at 8-under-par 136 with Chad Campbell one stroke back at minus-7.
Perry, who won the Colonial by six shots last week, has maintained his momentum from that victory. He coasted through the front nine with six straight pars to open his round at Muirfield Village.
At the par-5 seventh, Perry knocked his third within 15 feet of the cup. He then rolled in the birdie putt to get to minus-8. He parred the next two holes before heading to the back side.
Perry dropped a 9-iron within 15 feet at the par-4 10th to setup his next birdie. After a string of pars, he took advantage of the next par-5, the 15th. He slammed a 2-iron into a greenside bunker on his second shot before getting up-and-down for birdie.
The 42-year-old grabbed the lead with a birdie at the last. He knocked his 5-iron second just over the green, but recovered nicely as he chipped in for birdie.
'It was a good round of golf for me,' said Perry. 'I was happy with the way I played today. I am kind of still in that same rhythm and same mode. I was able to hit a lot of fairways, a lot of greens. I really wanted to shoot something in the 60s today just to get in position for the weekend. I was proud of my round.'
After missing the cut at the Byron Nelson Championship two weeks ago and carding seven straight rounds in the 70s, Perry has recorded six straight rounds in the 60s with 68 being his worst round.
'Everything that can go my way is going my way,' Perry said. 'The four- or five-footers that I need to make for par, I'm making right now to kind of keep the momentum and the swing going my way. Then I will make a 20-footer for birdie. It just seems like the momentum holes that you need to do something to keep your run going, I have been able to take advantage of.'
Goosen and Janzen shot matching rounds of 5-under 67 to share second place. Goosen notched back-to-back birdies from the fourth before dropping a shot at the par-3 eighth.
Around the turn, Goosen ran off three straight birdies from the 10th to get to minus-9. He rolled in a birdie at the 15th for his final birdie of the day.
'It's a funny game. Sometimes you feel like you are really hitting the ball great,' Goosen said. 'A couple of months ago, I'm really driving the ball well, hitting my irons great and I couldn't make any putts. These last few days I missed a lot of fairways and greens but got it up and down and made everything that I looked at. So that's really grinding it out there.'
Janzen, a two-time U.S. Open winner, notched three birdies in a four-hole stretch on the front nine to get to minus-8. On the back nine, Janzen bogeyed the 10th but came right back to birdie the next.
The 38-year-old notched another birdie at the par-4 13th. However he dropped a shot when he bogeyed the following hole. Janzen atoned for the error with consecutive birdies from the 15th, to grab a share of second place.
'I thought it played a little tougher today,' Janzen said. 'The wind was certainly much stronger today, which dried the greens and made them quicker.'
Charles Howell III, the first-round leader, Robert Gamez, defending champion Jim Furyk and Tiger Woods, a three-time winner here, share seventh place at 6-under-par 138.
The cut line fell at 2-over-par 146. Among those missing the cut were Sergio Garcia, plus-3, as well as host and course designer Jack Nicklaus, who finished at 4-over-par 148 despite a birdie on the 18th hole.