Zambia, whose first two games ended in 5-0 hammerings, finished third in Group C, with Japan top after their 4-0 win over Spain. Costa Rica finished bottom and did not pick up a point in their three matches.
Defender Lushomo Mweemba scored the fastest goal of the tournament so far, with a spectacular volleyed effort at two minutes and 11 seconds, and captain Barbra Banda doubled the lead from the penalty spot just after the half-hour mark.
Zambia's Lushomo Mweemba celebrates the first goal of the match during the Women's World Cup Group C soccer match between Costa Rica and Zambia in Hamilton, New Zealand, July 31, 2023.
Melissa Herrera cut the deficit two minutes after the break, and Costa Rica pushed for an equalizer, but substitute Racheal Kundananji netted the third in stoppage time to ensure Zambia's debut World Cup campaign ended on a high.
"It's a historic day," Banda said. "We've had a lot of support back home so we wanted to win today ... It was not an easy game for us. It was a battle."
Zambia were awarded the spot kick after Banda went to ground inside the six yard box and the forward stepped up to calmly slot the ball into the bottom left corner, scoring the 1,000th goal in Women's World Cup history.
"I've been practicing penalties in training so I was confident," Banda added. "At the same time, I was nervous ... carrying the hopes of thousands of people back home. It was an honor for me to take that penalty."
Playing at their second World Cup, Costa Rica were still searching for their first win in the competition and scored two minutes after the break, when forward Herrera bundled the ball home after goalkeeper Catherine Musonda was unable to clear it.
Costa Rica appealed for a penalty when midfielder Priscila Chinchilla collided with Musonda in the box, but were denied after a lengthy VAR check when replays showed forward Sheika Scott was offside in the build-up.
Herrera had the ball in the net again with around 20 minutes remaining but was ruled offside, and Valeria Del Campo fired wide before, against the run of play, Kundananji scored from Banda's cross in stoppage time to seal a historic result.
"We are very happy to win our last game in the tournament," Zambia coach Bruce Mwape said. "Everybody worked very hard to come up with this positive result... I hope next time we'll come (to a World Cup) with a different approach."