Lepp, who took the top spot in qualifying with a two-day total of 5-under 135, was nearly sent home on the first day of match play at historic Merion Golf Club.
Reifers took a 1-up lead to the 18th hole, but Lepp came up with a birdie to extend the match. Lepp then hit a wedge to 3 feet on the first extra hole and drained the putt to advance.
'When I hit the wedge in, I thought, 'Oh, it looks good,'' said Lepp. 'It felt good. It just spun down the hill perfectly. I didn't feel real great with the putter today, so it was nice to have that close right-edge putt.'
Lepp, a 21-year-old Canadian who will be a senior at the University of Washington, is the reigning NCAA individual champion. He will next face Dane Burkhart, who posted a 1-up victory over John Holmes.
Korey Mahoney, the second seed after stroke-play, also moved on with a 5-and-4 victory over Carter Henderson.
Five United States Walker Cup members advanced to the second round, as Brian Harman, Billy Hurley, Nicholas Thompson, Matt Every and Anthony Kim all won first-round matches Wednesday.
Hurley, seeded 61st, knocked off Charlie Beljan, 5-and-4. Beljan, who held the lead after the first round of stroke-play, was the highest-seeded player to lose on Wednesday.
The second and third rounds are scheduled for Thursday, with the quarterfinals on Friday and the semifinals Saturday. The 36-hole final will be played Sunday.