Last season's Premier League winners have begun their title defence a little sluggishly and found themselves 1-0 down to the Black Cats after just five minutes.
And United trailed by that score for 50 minutes at the Stadium of Light before teenage debutant Adnan Januzaj scored twice in quick succession to secure the three points.
Jones told MUTV: "That was the sign of champions out there. When your backs are against the wall and everyone's raising questions, a performance like that puts the record straight.
"Everyone dug in. It was a great performance and a massive three points.
"We were put on the back foot right from the first minute, and perhaps we didn't get out of the traps as well as we should have done.
"They were fired up, and perhaps we didn't expect it quite as much as we should have in the first 10 minutes. But, once we got to grips with the game, I thought we played some terrific stuff."
Januzaj clearly has a very bright future and Jones added: "He's a massive talent and he's got a lot of ability. If Gareth Bale scores one like the second goal, everyone's raving about it.
"He's a bubbly lad and a fantastic footballer, but he's a level-headed guy as well.
"He knows what he has got to do. He has to keep his head down and, if he keeps playing like that, he is going to hit the heights."