Lambert delighted with tactically terrific Villa
Gabriel Agbonlahor scored the only goal of the game in the eighth minute and Philippe Senderos and Andreas Weimann had chances to extend the visitors' advantage in the early stages.
An exceptional defensive display ensured another memorable trip to Merseyside for Lambert's men, who were pegged back for a 2-2 draw last season having won 3-1 on Liverpool's turf two years ago.
"Tactically it was fantastic," said Lambert, who has overseen Villa's best start to a league campaign for 16 years following three victories and a draw from their opening four fixtures.
"You've got to have lads who will go and try to carry it out and right from the off they were outstanding.
"We started with two up front and then we changed it - it worked.
"In the first half we had two or three chances. Philippe should have scored with his header; Andi Weimann's shot, I don't know if that was going in, the one that got cleared.
"It was a fantastic performance and a fantastic result."
Liverpool struck the post late on through Philippe Coutinho but Villa goalkeeper Brad Guzan enjoyed an unexpectedly quiet game as his back four excelled.
Lambert was also keen to highlight the defensive responsibility shown throughout his team, paying particular credit to midweek England debutant Fabian Delph, new arrival from Manchester United Tom Cleverley and their midfield colleagues Ashley Westwood and Kieran Richardson.
"We've worked a lot in training and the lads have grasped it, what we're asking them to do," said the Scot.
"There were great energy levels. Cleverley came in and I thought he was outstanding.
"Delph is just carrying on from where he left off the other night and Westwood is a lad who's unfairly not spoken about. His performances have been excellent.
"Richardson has come in - great. And Weimann has been great for me for the past few years.
"We've got legs in there and lads who want to do well. Right from Gabby to Guzan, defensively we were excellent."