The 19-year-old midfielder and the £6million striker had the game sewn up within 23 first-half minutes as a much-changed City side offered little resistance in front of a crowd of just 20,576 at the Stadium of Light.
They might have won even more comfortably had Maik Taylor not denied Kenwyne Jones with his legs, or had defender John Mensah's 57th-minute strike not been chalked off for a foul.
Sunderland were ahead within four minutes, Henderson sweeping home his first senior goal for the club from Jones' square ball to set the tone for a blitz which the visitors found irresistible.
It was 2-0 with 23 minutes gone when Campbell, who had already seen a close-range header deflected over by defender Giovanny Espinoza, made amends, beating Taylor to Andy Reid's inviting cross to glance the ball home.
To their credit, the visitors rallied briefly immediately after the restart, but it did not last, and they might have fallen further behind in a flurry of activity in the 53rd minute. First former Middlesbrough defender Stuart Parnaby had to get in a good block to keep out Reid's driven effort, and then Taylor had to pluck Lorik Cana's curling shot out of his top corner.