Manchester City star Haaland opened the scoring from the penalty spot in the 61st minute of Saturday's clash but Scotland hit back after he was substituted to seize the lead with two goals in two minutes.
Having netted his first goal in six games for club and country since his 35th English Premier League goal against Everton on May 14, Haaland was withdrawn by Norway coach Stale Solbakken in the 84th minute - and Scotland scored three minutes later through Gold Coast-born Lyndon Dykes.
With a minute of regular-time remaining, Scotland took the lead when Dykes passed for substitute Kenny McLean to score his first Scotland goal since 2019.
Defeat dealt a heavy blow to Norway's chances of qualifying from Group A.
Scotland are the group leaders with nine points as they aim to qualify for back-to-back European Championships for the first time since 1996.
Spain have three points from two games, including a loss to Scotland, and did not play on Saturday, while Georgia beat Cyprus 2-1 in the group's other match.
In Group J, Cristiano Ronaldo earned his 199th cap for Portugal, playing all 90 minutes of a comfortable 3-0 win over Bosnia-Herzegovina.
Bernardo Silva opened the scoring for Portugal, with Bruno Fernandes netting the other two.
Portugal have 13 goals and are yet to concede any in qualifying.
Slovakia are two points behind in second place after beating Iceland 2-1, while Luxembourg rose to third with a 2-0 win over Liechtenstein.
Belgium fought back to draw with Group F leaders Austria 1-1 thanks to a goal from Romelu Lukaku which cancelled out Michael Gregoritsch's deflected opener.
Azerbaijan drew 1-1 with Estonia in the group's other game, while in Group E the Czech Republic beat the Faroe Islands 3-0 to stretch their lead at the top to four points.
