The 15th seeded Iyer, who ousted top seed Montinee Tangphong in the third round, raced to a 4-2 lead in the first set before Engels stepped up and tied the count at 4-4.
"Engels served well," said Iyer of her Australian opponent who fired two aces to tie the count at 4-all in the first set. The Indian won the ninth game after Engels double-faulted twice and held her serve in the next game to win the set.
"I tried to keep my focus and played aggressively in the second set, attacking the net and hitting the ball harder. I really wanted to win," said the Madras-born netter, a high school student at the juniors Tennis Champions Center Academy in Virginia.
Iyer’s semifinal rival is fifth seed Chinese Chen Tan-Chong, who scored a 6-0, 6-2, victory over No. 13 Sanaa Bhambri of India.
Iyer, who played in the World Youth Cup in Czech Republic last year, will try to avenge her 6-7, 2-6 quarterfinal loss to Chen in a Group B tournament in India last December.
In the other match, No. 14 Lara Giltinan of Australia downed No. 10 Michelle Mitchelle of the US, 6-3, 6-3.
In the boys’ division, second seed Taiwanese Liu Tai-Wei survived unseeded Tom Rushby of Great Britain, 3-6, 6-4, 7-6 (3), to advance in the semifinals against sixth seed Adam Feeney of Australia.
Seventh seed Jamie Baker of Great Britain prevailed over fourth seed Suk Hyun-Joon of Korea, 6-4, 1-0 (ret.) to advance against No. 10 Karan Rastogi of India, who rallied past qualifier William Ward of New Zealand, 3-6, 6-3, 6-1.