Burke (16), a Mt Aspiring College pupil, clocked a personal-best 10min 9.89sec, but was outgunned by a string of North Island runners.
Taranaki's Hannah O'Connor (14) won the race, which was held as part of the annual Potts Classic meet, in a sizzling 9min 52.72sec.
Phoebe McKnight, of Lower Hutt, was 2.05sec back in second, while Deborah Paine, of Tauranga, was third in 9min 56.94sec.
Hill City-University sprinter Terry Collins-Hawkins was also in Hastings, and finished third in a tight 100m final.
After finishing second in his heat in a personal-best 10.88sec, Collins-Hawkins stopped the clock in exactly the same time in the final.
Hamish Gill, of North Harbour, won in 10.64sec, while Australian Jackson Miller-Gage was second in 10.77sec.
Collins-Hawkins also finished third in the 400m in 49.96sec. Australian Alexander Carew won in 48.02sec and Scott Burch, of Palmerston North, was third in 49.46sec.
New Zealand 1500m ace Nick Willis and 800m specialist Angie Petty started the year well by winning the men's and women's 800m feature races.
Petty, who has already qualified for the 800m at the Rio Olympics later this year, set a meet record of 2min 3.43sec on her way to a seventh consecutive title.
Willis, who sat behind defending champion Brad Mathas before sprinting past him down the home straight, won in 1min 49.88sec, his fastest time over 800m in almost three years.
Petty and Willis are expected to compete in the national 3000m championships in Wellington on Friday.
