Houghton took advantage of a free kick just outside the penalty area to send a right-foot shot into the left side of the net, getting the ball just inside the wall to beat New Zealand goalkeeper Jenny Bindon.
The New Zealanders, who have never won a match in the Olympics or the World Cup finals in women's football, controlled play early before Britain took over about midway through the first half, creating a series of dangerous scoring chances.
"It was a tough contest," Powell said. "Conditions were very difficult for both sides. It was a battle. We are really pleased to get the first game out of the way with three points."
The best chance before Houghton's goal had come in the first half when midfielder Anita Asante's header struck the post and just trickled out in the 34th minute, prompting Bindon to kiss the woodwork in appreciation.
Bindon had already made a difficult save on a long-range free kick taken by Houghton in the 21st. On the ensuing corner, forward Eniola Aluko had her shot blocked just in front of the goal, with Bindon already on the ground.
Asante also just missed with a header in the 36th from a corner, and Alex Scott's shot in the 38th went just wide after she cleared a defender inside the area.
New Zealand had one of its few scoring chances early in the second half, when Amber Hearn's free kick sailed wide but close to the goal in the 49th.
Britain continued to attack and substitute Ellen White missed a great chance in the 63rd when she broke clear into the area but had her shot blocked by New Zealand's Karen Carney.
New Zealand forward Sarah Gregorius nearly equalized in the 72nd after two British defenders collided when going for the ball. Gregorius ended up free on goal but only managed a weak shot into the hands of Britain goalkeeper Karen Bardsley.
Bardsley also tipped a shot from Hearn over the crossbar in the 84th.
"The players are devastated," New Zealand coach Tony Readings said. "But we've got a lot of positives to take from the performance today. We felt we could've won the game against this GB team."
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-AP