The Villains travelled north without a win in five games since beating Swansea City in mid-September, leaving Lambert’s men in 17th place.
However, Gabriel Agbonlahor made the vital breakthrough in the 57th minute when he latched onto Christian Benteke’s nod down and fired past Simon Mignolet from close-range.
“I thought the lads were fantastic,” Lambert told BBC Sport.
“They are a team that deserves credit. They have had their knocks in the last two years. We were down to the bare bones and there were some real good performances from them. I’m proud of them. I thought we deserved to win.”
The Black Cats came close to levelling when substitute Louis Saha headed narrowly over the crossbar, and Martin O’Neill admitted his side’s wayward finishing continues to hamper their progress.
“It just wouldn’t drop for us in the penalty area,” said O’Neill.
“We put an awful lot of pressure on them. Scoring goals has been a problem for us this season but it was not for the want of trying.
“Our creative players are finding it a little bit difficult at the moment.”
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