Six athletes qualified from each heat. The next fastest six from all heats, of which van Dalen was one, also went through.
Van Dalen ran a time of 4m 07.04s. The 23-year-old was 1.28s outside her Games qualifying time of 4m 05.76s. Ethiopian Abeba Aregawi won the race in 4m 04.55s on a slightly overcast London day.
"The last few hundred metres were a bit pushy and shovey," van Dalen said. "The race probably got away from me a bit in the last 200m but I'm pleased with my performance. I probably should have been more aware of people running in front of me.
"I came out and I could hear my family and friends cheering my name, then I saw them which was amazing.
"My coach told me to relax on the rails because when you're running fast you don't want to be running wide. I just kept praying throughout."
Britain's Lisa Dobriskey won the second heat in 4m 13.32s while Turkey's Gamze Bulut took the third heat in 4m 06.69s.
Wanganui-raised van Dalen emerged from relative obscurity to make the New Zealand team.
She has been based at Stony Brook University, a small college on New York's Long Island, for the past four years. She is the first woman to represent New Zealand in the 1500m since Toni Hodgkinson at Sydney in 2000.
Nikki Hamblin still holds the New Zealand women's 1500m record of 4m 04.82s.
