The 19-year-old Spanish tennis player had won his first Barcelona Tournament title last year by beating his compatriot Pablo Carreno in the final by a resounding 6-3, 6-2.
In the Pool-B match, Team India won its third consecutive win by performing brilliantly. The team, which had already made it to the semi-finals, secured the first position in the group with nine points.
Labuschagne, who is currently ranked No.1 batter in Test Cricket, has achieved a career-high rating, 937 points, in the latest ICC Test Batting Rankings.
Southee will lead the team on their forthcoming tour of Pakistan with Tests in Karachi, starting on December 26, then in Multan beginning on January 3.