Elsewhere, Bernardo Silva, Ruben Dias and Joao Cancelo all featured for Portugal as they maintained their fine start in Group J with a dramatic 1-0 win away to Iceland.
For Haaland and Norway, victory over the Cypriots was the perfect response to last Saturday’s disappointing 2-1 loss to Scotland and got their Group A campaign up and running.
The Norwegians had got off to a perfect start in Oslo as they took a 12th minute lead thanks to an effort by Ola Solbakken.
And City striker Haaland then doubled their advantage 11 minutes after the restart, firing home from the penalty spot after a VAR check had confirmed that Nicholas Iannou had committed a foul in the box.
Within four minutes Haaland had struck again, rifling in Martin Odegaard’s inviting assist to register what was his 24th goal in just 25 games for his country and his 61st effort overall since June last year as he rounded off a quite extraordinary season before being taken off with three minutes left.
Grigoris Kastanos’s injury time strike proved little more than consolation for the Cypriots.
The result leaves Norway with four points and moved them up into third place in the table.
Elsewhere, Bernardo, Dias and Cancelo all started as Cristiano Ronaldo marked his 200th international appearance by scoring an injury time winner for Portugal away in Iceland.
Chances had proved at a premium in Reykjavik with an Iceland side coached by former City defender Age Hareide proving durable and resolute.
Dias played for the full 90 minutes with Cancelo making way on 67 minutes and Bernardo coming off in injury time while the hosts were reduced to 10 men ten minutes from time when Willum Willumsson was sent off for a second bookable offence.
But just when it looked like a draw was inevitable, Ronaldo made the vital contribution, scoring in the 89th minute with a close-range tap-in to maintain Portugal’s 100 per cent record in Group J with 12 points from four games.
Meanwhile it proved a frustrating night for Ilkay Gundogan and Germany as they lost out 2-0 to Colombia in a friendly played in Gelsenkirchen.
The South Americans had taken an early second half lead thanks to a 54th minutes strike from Liverpool’s Luis Diaz.
Gundogan played for 80 minutes before making way and six minutes from time Colombia sealed victory when Juan Cuadrado converted a penalty.
