With extra time looming the Swede nodded Ander Herrera's cross past goalkeeper Fraser Forster to score his 26th goal of the season in all competitions and secure Jose Mourinho's first trophy since the Portuguese coach took charge.
United had taken a 2-0 lead with Ibrahimovic's free kick and Jesse Lingard's shot but Southampton striker Manolo Gabbiadini's double either side of halftime breathed life into the showpiece match leaving the stage set for Ibra to snatch the winner.
