Bogan, 59, fell 1-down when Bill Heldmar birdied the first hole of their match. But Bogan won five holes in a row after that to move 4-up, and later clinched the victory with wins at the 13th and 14th holes.
'I was putting pretty good -- kind of silly good -- there for a minute,' Bogan said. 'My putting has been good all week, and normally that's pretty shaky. But every now and then, I can get it smoothed out a little bit.'
Four previous USGA champions were among the 32 players who advanced to the second round of match play.
Past Senior Amateur winners Greg Reynolds (2002) and Mark Bemowski (2004) moved on with slim victories. Reynolds edged Steve Earsley, 1-up, and Bemowski beat Joe Bartlett, 2-up.
Bill McDonald, the 1964 U.S. Amateur Public Links Champion, was a 1-up winner over Martin West, while 1972 U.S. Amateur champion Vinny Giles needed 22 holes to defeat Gene Ryzewicz.
There will be two rounds of match play on both Tuesday and Wednesday. The 18- hole final will take place Thursday.