Larsson, who represented Britain as they fielded men's and women's handball teams for the first time at an Olympics at London 2012, found the net eight times in Lavis.
That was two more than Italy's top scorer Demis Radovcic, who scored six goals, as Italy edged past Britain 37-26 having previously beaten them in 47-23 in Scotland back in April.
Britain's hopes of advancing from the first phase of qualifying and into the second were already over ahead of the clash having lost twice to Greece as well as once to Italy in their group.
However of all the matches, the last was their closest yet with Larsson scoring three times in the opening eight minutes before Italy went into half-time leading 18-13.
They eventually ran out 37-26 winners with Sebastien Edgar and Mark Hawkins both contributing five goals each and Aston Lang scoring three on his debut.