The two sides meet again in Budapest on Sunday for the second leg, with Hungary looking for a first major tournament appearance since 1986.
Norway were nearly ahead within the opening five minutes, but former Crystal Palace goalkeeper Kiraly did brilliantly to turn over Per Ciljan Skjelbred’s effort from point-blank range.
Kleinheisler forced a fine save out of Orjan Nyland with a first-time volley at the other end, but the 21-year-old got the better of the Norway goalkeeper after 26 minutes.
Hungary nearly doubled their lead after the break through Adam Szalai, but his effort from an angle was saved well by Nyland low down to his right.
Norway dominated possession throughout, and had 16 corners to Hungary’s none, but their best chance did not come until the 87th minute.
First, Stefan Johansen broke through on goal on the left, only to see his low shot saved well by Kiraly, and as the ball looped up forward Helland, the midfielder could only head onto the crossbar with an open goal to aim at.
** Argentina’s home World Cup qualifier against Brazil in Buenos Aires was postponed for 24 hours after heavy rain an hour before the scheduled kickoff in the Estadio Monumental.