Gabriel Agbonlahor capitalised on a dreadful mistake from Sunderland captain Lee Cattermole in the 15th minute, dispossessing the midfielder 25 yards from goal before rounding Vito Mannone and slotting home to earn Villa's first win in six Premier League games.
Christian Benteke, without a goal in 11 games, could have doubled the lead in the second half but saw his effort cleared off the line by Phil Bardsley, before substitute Marc Albrighton blazed over when clean through on goal late on.
"I'm delighted," Lambert said.
"I thought we deserved it and could have run out more comfortable winners. We should have had at least three or four with the chances we had.
"It was always going to be tough up here but I felt the Swansea game gave us a platform to try and build from."
Sunderland's Fabio Borini had an equaliser ruled out seven minutes after the break for a tight offside decision, which Lambert insisted he could not call from his standpoint, but the manager reserved special praise for his match winner.
"I couldn't see," he said.
"It's hard to see from where I'm standing but the best one in the place to see it is probably the linesman.
"(Agbonlahor's) was a massive goal. When he's got speed like that and he's on that sort of form, he's excellent."
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