Zahringer, 50, of New York, NY, knocked off Jay Poletiek on the 19th hole after blowing a two-up lead with just two holes remaining.
'It was kind of rag-tag all day,' said Zahringer. 'I have to play better.'
Zahringer has played in 16 events this summer -- including the U.S. Amateur and Walker Cup Match, which have worn him down.
'You've got Tiger [Woods] who plays in about 16 events a year,' said Zahringer. 'People look at that and say, 'You've only played 16 events.' For us [amateurs], that's probably equivalent to 30 because we're working when we're not playing.'
Davis, 36, of Norman, OK, cruised passed Danny Gurley, 5-and-4 to reach the second round.
Davis, a golf course architect, qualified with a 4-under 137 and said he didn't feel any pressure being the medalist.
'Once you get into match play, everyone's on the same ground,' he said. 'Match play is fickle where you can run into a buzz saw. Hopefully I'll be that buzz saw.'
Other key matches in round one were Trip Keuhne of Dallas, Texas, defeating Tyler Crawford, 3-and-2, while two-time winner Tim Jackson lost to Steven Galko, 2-and-1.
Kuehne took the lead on the 14th and never looked back, although his bogey- free streak of 43 holes ended on the par-4 eighth with a three-putt.
'I wasn't making very good shots,' he said. 'I just tell myself that I've got to give myself a chance.'
Also advancing was 1995 champion Jerry Courville, who defeated Mark Love, brother of PGA Tour star Davis Love III, and Steve Irwin, son of three-time U.S. Open champion Hale Irwin, who eliminated John Wright.
Play continues on Tuesday with second and third round action and concludes on Thursday with the semifinals and championship matches.
The U.S. Mid-Amateur is one of 13 national championships conducted annually by the United States Golf Association, 10 of which are strictly for amateurs.