Lee, who was 4-down after four holes, birdied the 17th to gain his first lead of the match against Tway. Lee will face Philip Francis in Saturday's 36-hole final.
Francis won the first five holes of his match against Andrew Putnam and held on for a 4 and 3 win.
Lee, 15, gained the semifinals with a 2-up win over Danny Lee (no relation). Tway gained his quick 4-up lead with two birdies and two bogeys by Richard Lee.
Tway bogeyed the sixth, but came back with a birdie on the seventh. Lee eagled the par-five eighth, then Tway bogeyed the next two holes as his lead dipped to 1-up.
A birdie on the 11th gave Tway a 2-up cushion, but Lee rallied. He took the 13th at Rancho Santa Fe Golf Club thanks to a double-bogey by Tway. Another double-bogey by Tway on 16 evened the match.
Lee birdied the par-3 17th to take a 1-up lead. He claimed the match as the pair halved 18 with pars.
Francis needed 20 holes to beat Sihwan Kim, who won the 2004 U.S. Junior Amateur, and move into the semis. Last year in this event, Francis needed 19 holes to beat Kim.
Putnam started bogey-bogey to fall 2-down. Francis birdied the next two to extend his lead to 4-up.
The 17-year-old Francis saw his lead grow to 5-up as Putnam bogeyed the fifth. Putnam rallied to birdie three straight holes from the sixth to get within 2- down.
Putnam tripped to a bogey on the 10th to dip back to 3-down. The pair halved their next four holes, but Putnam's double bogey on the 15th gave Francis the win.
Saturday's 36-hole final will start at 11:00 a.m. (et) with the second 18 holes slated to start at 3:45 p.m.