New Zealand forward Chris Wood opened the scoring from just in front of the goal after a corner in the 17th minute at Old Trafford, and Egypt forward Mohamed Salah equalized from close range following a counterattack in the 40th.
Both teams had great chances at the end but couldn't capitalize on them.
Egypt and New Zealand had lost their opening matches and will need victories in the final round to advance. They have one point each after two rounds. New Zealand will face Brazil and Egypt will play Belarus. Brazil and Belarus, with three points each, will play later in Manchester. Only the top two teams in each of the four groups advance.
Knowing the draw wouldn't help much, both teams pressed forward in the final minutes and there were good scoring opportunities for both sides.
Emad Meteab could have given Egypt the win in injury time but missed an open net after clearing two defenders and the goalkeeper inside the area. His teammates dropped to the ground behind him in despair.
Ahmed Fathi also almost scored for the Egyptians near the end, and New Zealand forward Shane Smeltz couldn't get a shot off despite a great one-on-one chance at the other end as time was about to expire.
The fans nearly filling Old Trafford gave the teams a standing ovation at the end.
"It was an excellent game for the supporters to watch," New Zealand coach Neil Emblen said. "In the second half both teams were desperate for a win. We had chances up to the last minute. I think we needed to win the game more than Egypt needed because now we are the ones who will face Brazil."
New Zealand was trying to win its first match in an Olympic or World Cup tournament. This is the team's second consecutive time participating in the Olympics. It has also played in two World Cups, in 1982 and 2010.
The Egyptians came to the London Games hoping to restore some of the country's football pride nearly six months after the stadium riot that killed more than 70 people in the Port Said tragedy.
New Zealand opened the scoring after defender Tommy Smith headed a corner toward the goal and Wood easily redirected the ball into the net from close range.
Egypt put on pressure after conceding the goal and started creating more chances.
The equalizer came when team captain Mohamed Aboutrika made a perfect cross from the right side and Salah sent the ball into the net from just in front of the goal. New Zealand goalkeeper Michael O'Keeffe touched the ball but couldn't keep it from going in.
New Zealand appealed for offside and replays showed it was a close call when Aboutrika made the pass to Salah.
Salah plays for Swiss club FC Basel and is the only member of Egypt's Olympic squad in European football.
Egypt lost 3-2 to Brazil and New Zealand 1-0 to Belarus in the opening round.
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