Southampton overcame a late concession to outlast Everton in penalty kicks at Goodison Park to round out the League Cup’s Round of 16.
Saints will travel to Leicester City in the next round.
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But Angus Gunn saved Walcott in penalties as Saints won 4-3.
Ings now has four goals in seven matches for Saints, on loan from Liverpool ahead of a permanent move next summer.
He’s twice scored against the Reds’ Merseyside rivals since moving to Saints, and his four career goals against Everton are his joint-highest against a single opponent (Huddersfield Town, Birmingham City).
Saints manager Mark Hughes puffed his chest after the win.
“We played the more progressive football, and had sustained periods of control. It showed what a good team we are,” he said. “Obviously it is nerve-wracking when it goes to penalties, but we got the job done. … We weren’t going to be denied tonight, there was real focus in the team and we wanted to get through this tie.”