Having earlier saved from Keith Andrews and Roque Santa Cruz, Jones produced five crucial stops from substitutes David Dunn and Jason Roberts, the last of them five minutes into injury time, in a dramatic conclusion to the game.
Southgate: "He is a good goalkeeper. Ross has done very well for us, but it was time for him to have a break.
"Brad is an excellent goalkeeper. The types of saves he made today are what he is particularly good at. His reflexes are terrific."