Striker Christian Benteke scored twice either side of Andreas Weimann's well-worked goal before Steven Gerrard struck a late consolation.
It was the first time Villa had scored more than once in any half of league football this season and extended their unbeaten run to five matches with only a second away win in 17 league games on the road.
Only a fifth Anfield victory in 34 visits also almost doubled their league away goals tally, which now stands at seven.
Lambert said: "I think the whole performance was fabulous, the goals were excellent as was the way we defended.
"I thought we were excellent. The goals were brilliant: the second goal, with the movement and the backheel, especially.
"Benteke has been unbelievable while Andy Weimann knows where the goal is, he's a natural finisher and his enthusiasm and work ethic are second to none.
"The back three were terrific and put their bodies on the line when they had to.
"I am pretty sure Liverpool will give anyone a game here. It is just about trying to hold your nerve and trying to see it through, which is what we have done."
- Sports & Recreation
- Andreas Weimann
- Christian Benteke
- Steven Gerrard