The 20-year-old, earning his third cap for his country, helped his team get off to a flying start by teeing up striker Jorgen Strand Larsen for a third minute opener.
Our Academy graduate did all the hard work, playing a one-two from a corner and dribbling along the byline into the area before hitting a low hard cross that Larsen diverted in.
Bobb went one better in the 24th minute by dribbling and firing inside the near post from the edge of the box for his first ever goal in senior football.
It’s the latest highlight of a promising season for Bobb, which has seen the creative midfielder feature on seven occasions for Pep Guardiola’s City so far.
Erling Haaland was a second-half substitute in this match for Norway but didn’t find the net in his 45 minutes on the pitch.
Ahead of coming on, the striker had been quick to congratulate Bobb as the two sides returned to the pitch for the second period.
Haaland however is likely to start when Norway play Scotland at Hampden Park in Glasgow on Sunday.
Elsewhere, Bernardo Silva played 61 minutes as Portugal beat Liechtenstein 2-0 thanks to goals from Cristiano Ronaldo and Joao Cancelo.
Ruben Dias was an unused substitute in Vaduz.
The result extends Portugal’s perfect record in EURO 2024 qualifying to nine wins.
They will complete their campaign against Iceland on Sunday knowing their place at the tournament in Germany next summer is already secured.