Bouchard, ranked 59th in the world, fell 6-4, 2-6, 6-3, but not before the Montreal teen staved off four match points to make things interesting in the final game, drawing cheers from the New York City crowd for her winners.
Bouchard was unable to match her third-round showing from Wimbledon as she broke Kerber's serve six times on 14 chances but lost her own serve on seven occasions and committed seven double-faults.
After a day of rain on Wednesday, the schedule was jammed for Canadians, with three more taking to the court for second-round matches later.
Aleksandra Wozniak of Blainville, Que., was playing only her second match since March after last autumn's shoulder injury, facing a huge task against double Grand Slam champion Victoria Azarenka.
In the men's draw, 10th-seeded Milos Raonic of Thornhill, Ont., faces Spain's Pablo Andujar, while Frank Dancevic from Niagara Falls, Ont., takes on Spain's Tommy Robredo.
No. 4 Errani falls
In other women's second-round action around Flushing Meadows, Flavia Pennetta ousted fourth-seeded Sara Errani 6-3, 6-1.
The two are close friends and teammates on Italy's Fed Cup team. Pennetta was the first Italian woman ranked in the top 10, but has fallen to 83rd. Her slide began when she missed the end of last year, including the U.S. Open, with a right wrist injury.
Errani was the French Open finalist and a semifinalist at the U.S. Open last year but has made it past the second round in only one of the four majors in 2013.
Errani's doubles partner, No. 10 Roberta Vinci, defeated Lucie Safarova of the Czech Republic, 4-6, 6-1, 6-2. This year's Wimbledon runner-up, 16th-seeded Sabine Lisicki, beat Paula Ormaechea of Argentina, 6-2, 6-3.
Top-seeded defending champion Serena Williams took the court after Pennetta for a rescheduled match against Galina Voskoboeva.
Also due to play Thursday on the men's side were Roger Federer, Rafael Nadal, David Ferrer.