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Haaland scored Norway’s second and third goals in the 48th and 58th minutes, after substitute Marcus Holmgren Pedersen had opened the scoring in the 43rd minute.
Crystal Palace forward Ismaïla Sarr scored both of Senegal’s goals, the first in the 53rd minute and the second in stoppage time (90+3).
Norway, which had already beaten Iraq 4-1 in their opening match, recorded a second consecutive victory to move on to six points and secure qualification for the round of 32.
They sit second in Group I, trailing leaders France on goal difference after France defeated Iraq 3-0 earlier in the day.
Norway and France will meet in the third and final group match on the 26th, in a decisive encounter to determine the group winners.
Norway must win to finish top of the group, while France needs only a draw to retain their first place.