Peliwo edged out Britain's Liam Broady 6-2 2-6 7-5 to add the trophy to the Wimbledon title he won in July.
The 18-year-old Canadian was the first male to reach all four Grand Slam junior finals in the same year since Stefan Edberg won all four in 1983 and the first to win Wimbledon and the US Open back-to-back since Bulgaria's Grigor Dimitrov in 2008.
"I have to say I'm a lot more relieved now than I was at Wimbledon," Peliwo said. "At Wimbledon it was just excitement and right now I just got a huge weight off my shoulders."
Peliwo said he hoped to make strides into the men's game but does not expect to fly up the rankings immediately.
"I've got some big expectations for myself but I'm not putting pressure to have great success right off the bat going into the pros," he said. "I'm going to take it step by step and get my ranking up slowly - or quickly if I can."
Thirteenth seed Broady, 18, could only send down one ace to his opponent's eight.
He also committed 14 double faults against the second seed's five.
He was looking to match the achievement of Oliver Golding, who won the boys' singles at Flushing Meadows last year, and Andy Murray, who won it in 2004.
Another Briton, Kyle Edmund, won the boys' doubles with Portuguese partner Frederico Ferreira on Saturday night 5-7 6-4 10-6 over Australians Nick Kyrgios and Jordan Thompson.
Unseeded Crawford outgunned 12th seed Anett Kontaveit 7-5 6-3 to win her first Slam title.
Crawford trailed 4-2 in the first set before storming back, slamming winners on both sides to upset the Estonian, who was also appearing in her first final.
"I thought she came out playing really well," the 17-year-old Crawford said. "As the match went on I started serving better and playing better overall. It feels awesome."