The 32-year-old Dutchman had been left out of the squad for the two previous games after a difference of opinion with the manager following his non-selection on returning from a one-match ban against Everton on New Year's Day.
At one point, it appeared he could leave the Riverside Stadium, but Southgate knew he could depend upon a response.
He said: "I was delighted with him. You know with him that he is a winner, that he is an excellent professional and that when he was asked to play again, he would give it everything.
"He capped it with a goal and he showed the character he has."