The Nordic nation took the lead in the 25th minute with a goal from Håvard Nordtveit. The 24-year-old defender headed the ball into the net from a Stefan Johansen cross.
The first-half was a scrappy affair, littered with fouls and freekicks and Norway was content with most of the best chances, culminating in the goal ahead of the half-time whistle.
The second-half saw Azerbaijan pushing for an equalizer as Norway sought to put the game out of their opponent's reach.
Neither team created many clear-cut chances and Norway won the match, happy to take away the three points.
After the match, goal scorer Nordtveit, said to MAX: "We knew it was going to become a tough match. We came here to take three points, and it's truly wonderful that we got them."
Teen soccer sensation Martin Ødegaard was not in the squad for this game.
Norway's next Euro 2016 qualifier match is away to Croatia on March 28th next year.
Croatia drew 1-1 with Italy in their Group H crunch match on Sunday. Both teams still lead the table.