Bogan completed the 36-hole stroke-play portion at 5-under-par 137.
'Normally, the thing I do the best is hit it short and straight, but today I had two lost balls in the bushes,' said Bogan. 'I was pretty happy with 71 after giving four strokes away.'
Bill Zylstra, whose first-round 65 was a record for this event, struggled to a 2-over 73 in round two. He shared second at minus-4 with Paul Simson, a co-medalist at both the 2004 U.S. Mid-Amateur and last year's USGA Senior Amateur.
'With match-play events, you've got to play well, and if you have somebody playing well against you, you've got to play a little bit better,' said Simson. 'That's just the nature of the beast.'
Erik Myrmo, Thomas McGraw, Bill McDonald, Lee Jeberjahn, David Stanfield and Michael Puls shared fourth place at 1-under-par 141 at Flint Hills National Golf Club.
Bill Heldmar won a 10-man playoff to earn the final spot in match play.
Mike Bell, the 2006 champion, missed the cut for the match play portion by six strokes. He became the first defending champion to miss the cut in nearly 20 years.
The top 64 players advanced to Monday's first round of match play. There will be two rounds on both Tuesday and Wednesday, while the 18-hole final will take place Thursday.