Colombia’s hopes of a famous win appeared to be over when Alexandra Popp cancelled out Linda Caicedo’s opener with a late penalty.

But with seconds remaining, Vanegas found the bottom corner with a powerful header from a Leicy Santos corner at the Sydney Football Stadium.

Germany carved out the best opportunity of the first half when Popp volleyed over the bar.

Colombia broke the deadlock in stunning fashion six minutes into the second period when Caicedo showed great footwork before curling home.

With just a minute left of normal time, Colombia goalkeeper Catalina Perez brought down Lena Oberdorf in the box.

Popp made no mistake from the spot as she fired down the middle.

She looked to have rescued a point for Germany only for an unmarked Vanegas to climb high and head in the winner for Colombia.

Co-hosts New Zealand have been knocked out of the tournament following a 0-0 draw with Switzerland in Dunedin Stadium in Group A.

Jacqui Hand went the closest to scoring when her first-half shot hit the woodwork as New Zealand became the first host nation to exit in the group stage of a Women’s World Cup.

"We knew if we win, we would go through," said New Zealand coach Jitka Klimkova.

"The result unfortunately didn't go our way, but the performance from our players was another very solid performance on the World Cup stage, and I'm very proud of our team and what we've done during this World Cup."

Switzerland, meanwhile, will progress to the last 16 along with Norway who thrashed the Philippines 6-0 thanks to a hat-trick from Sophie Roman Haug at Eden Park in Auckland.

Norway had been bottom of Group A having failed to score in their draw with Switzerland and defeat to New Zealand but managed to find their shooting boots just in time to seal their place in the knockout stages.

Haug netted the opening two goals inside the first 17 minutes before Caroline Graham Hansen fired home the third with a 25-yard strike on the half-hour mark.

Norway’s dominance continued after the break as Philippines’ Alicia Barker put the ball in her own net.

Guro Reiten dispatched a penalty for Norway’s fifth goal before turning provider with a cross for Haug to complete her hat-trick in injury-time.

History was made at the Hindmarsh Stadium in Adelaide as Morocco sealed their first-ever win at a Women’s World Cup.

Ibtissam Jraidi’s sixth minute diving header was enough for Morocco as they defeated South Korea 1-0 in Group H.

"We are just so pleased our efforts have paid off," said Jraidi.

"This victory is for Morocco and Arabs, it's the fruit of our hard work."

Competition is due to continue tomorrow with co-hosts Australia facing reigning Olympic champions Canada and Republic of Ireland tackling Nigeria in Group B as well as Japan taking on Spain and Costa Rica meeting Zambia in Group C.