Iceland finished second in the group behind Switzerland who qualified automatically for the 2014 finals in Brazil.
Kolbeinn Sigthorsson put Iceland in front after 12 minutes when Tore Reginiuseen played him onside and he fired the ball past Rune Jarstein.
Daniel Braaten levelled for Norway on the half-hour, holding off a defender to slot home from close range.
Sigthorsson and Birkir Bjarnason could have put the game out of reach for the visitors in the second half but instead hundreds of Iceland fans had to wait until the final whistle to celebrate the team's achievement with the players.
Xhaka gave the hosts a 1-0 win when he ran on to Blerim Dzemaili's pass and fired a diagonal 25-metre shot on the turn into the far corner in the 74th minute.
Needing at least a point plus a favourable result in the match between Norway and Iceland, Slovenia created plenty of openings in an end-to-end second half as Switzerland also looked for the win despite having secured top spot.
Kevin Kampl, Slovenia's most creative player, had the best chance to put them ahead when he intercepted a pass, burst forward and saw his shot saved by Yann Sommer.
Slovenia, who played at the 2002 and 2010 World Cups, became increasingly open at the back as they pressed for a goal and, after surviving several near misses, were finally sunk by Xhaka's outstanding effort but with Iceland drawing they would have needed to win to go through.
In the group’s earlier match Albania and Cyprus, fifth and sixth respectively, played out a goalless draw in Nicosia.