Relieved Lambert praises Villa
The win comes after a difficult start to the season for Villa, which has seen them collect just one win from their first eight games before their triumph at the Stadium of Light.
And Lambert was thrilled with his side's efforts, describing the victory as "massive" as Villa look to kick-start their season.
"That was great. I thought the lads were absolutely fantastic," he said.
"As a whole I thought that was our best performance. We played well against Swansea and West Brom in parts. I thought we were outstanding overall.
"To come to a place like this and win the game I thought it was deserved."
Lambert also reserved praise for young midfielder Ashley Westwood, who was handed his first league start in the match, and also praised the performances of strikers Christian Benteke and Gabriel Agbonlahor.
"We were down to the bare bones and there were some massive performances in there," he said.
"Ashley Westwood - in his first game at this level - was absolutely outstanding.
"You'd think Ashley had played at this level for about five years. He was excellent. For someone to come from Crewe and slot in like that and play like that, he was outstanding.
"I thought Christian Benteke was unplayable at times. Gabby is right on the top of his game at the minute."
Meanwhile, Sunderland manager Martin O'Neill described the defeat as "tough to take", as the Black Cats once again failed to win.
O'Neill's side have now won just one game in their last 17 but the Northern Irishman is confident his side will eventually turn it around.
"It was particularly difficult really," he said.
"We threw everything at them today (but were) unable to break them down and unable to score a goal.
"We had so many balls in the area, you could hardly have counted all the chances, but you just need a break and I believe it will come."
"It's been a difficult time and we have got to see it through, but the players are capable of doing that."