Spurs went ahead once Tanguy Ndombele’s shot deflected in off visiting defender Jack Stephens, before Shane Long created it 1-1 once James Ward-Prowse’s effort had been parried by Hugo Lloris.
Danny Ings curled an attempt past Lloris to place the Saints ahead, however Lucas Moura equalized with a strike from eighteen yards.
Spurs won the tie once Son Heung-min converted an 86th-minute penalty.
He had been fouled by Southampton goalkeeper Angus Gunn once a fine pass from substitute Dele Alli had created the chance,
For the Saints, midfielder Ward-Prowse was carried off on a stretcher within the half with a suspected knee ligament injury.
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