Saints chief Ronald Koeman was forced to pitch the 23-year-old into action for his first appearance of the season at Selhurst Park last Saturday when regular number one Maarten Stekelenburg was ruled out because of a toe injury, while Fraser Forster is working his way back from a long-term knee injury.
And Gazzaniga's impressive performance in the 1-0 defeat means the manager will have no qualms about keeping him in the team on Saturday.
Koeman has been boosted by the return to fitness of Graziano Pelle, who is expected to start on Saturday. Pelle was a substitute during last week's defeat at Palace, when Koeman played a more defensive team.
On Saturday, the manager is likely to revert to his more familiar 4-3-3, which could mean recalls for James Ward-Prowse and Dusan Tadic. Like Forster, fellow long-term absentees Jay Rodriguez and Florin Gardos remain sidelined with respective ankle and knee injuries.
Koeman is hoping his side can get back to winning ways after a run of five fixtures without victory in which they have conceded 12 goals.
Looking ahead to the game against former Saints boss Mauricio Pochettino's Spurs, he said: "If you win you get up in maybe five or six positions in the table, if you don't win two in a row you fall back.
"I think it's more close than ever this Premier League so far."