Norbäck played three Davis Cup matches for Sweden, all in the 1977 tournament, the first a win in a doubles rubber against Monaco with Douglas Palm early in the campaign.

The youngest player in either team, Norbäck partnered with Rolf Norberg in the doubles, with Sweden needing a win over the Italian pairing of Paolo Bertolucci and Adriano Panatta to keep the tie alive.

In the reverse singles, Norbäck replaced Rolf Norberg for a dead rubber against Antonio Zugarelli and was able to secure a consolation win for the Swedes.

He did not drop a set all tournament, with wins over Georges Goven, Lajos Levai, Juan Ignacio Muntañola, Nicola Spear, then in the final Jacek Niedźwiedzki.

Due to meet Manuel Orantes in the second round, he had spent the day with friends in New Hampshire, as a conversation with the referee-in-chief had left him under the impression his match was to be played late in the evening.