The 32-year-old striker turned home Alex Morgan's 27th-minute cross to give her side the advantage in a game they controlled but failed to kill off until substitute Sydney Leroux made sure at the death.
Last year's beaten World Cup finalists won with something to spare and will head into their semi-final at Old Trafford on Monday with hopes of a third successive gold medal very much alive.
The USA dominated throughout, pinning the Kiwis back into their own half for long periods with front two Wambach and Morgan repeatedly threatening to breach their defence.
They perhaps should have gone ahead with just 10 minutes played when Morgan ran on to Abby Erceg's miscued clearance and rounded goalkeeper Jenny Bindon, only to shoot wide of the far post, and Wambach side-footed harmlessly wide from Megan Rapinoe's driven cross seven minutes later.
However, the deadlock was broken after 27 minutes when Morgan got in on the left and drilled the ball across goal for Wambach to turn home at the far post.
Morgan could have ended the game as a contest within three minutes of the restart when she robbed Erceg and drove into the penalty area, but she blasted into the side-netting with just Bindon to beat.
The US striker stabbed another shot straight at Bindon after the New Zealand defence had struggled to clear a 58th-minute Rapinoe free-kick, and the keeper had to come from her line to deny the same player one-on-one four minutes later.
American keeper Hope Solo had to make a rare 76th-minute save from full-back Ria Percival's long-range strike, but Leroux's calm finish after 87 minutes sealed the win.