The result lifts Villa above Newcastle United in the Premier League table on goal difference, while also increasing the gap between themselves and the relegation zone to five points.
Hat-trick hero Christian Benteke will dominate the headlines, but Lambert was quick to give credit to a number of other players and also hailed the contribution of the fans.
"It was a fantastic atmosphere, the crowd have been brilliant since I've been here. I'm delighted for them because they come in their thousands to watch us. It's great credit to the players and staff, that was a massive performance and a big win for us," said Lambert.
"I thought Christian Benteke getting man of the match was always on the cards but I thought Matty Lowton was fantastic. Brad Guzan has been brilliant all season too, he sets himself high standards.
"The goal difference has swung back again, I have to give them unbelievable credit for that. I'm really proud of them. They have been playing like that for months, our form has been very good. They way we have been playing has been encouraging, I never had any trepidation."
Villa's three remaining games this season are against Norwich City, Chelsea and Wigan Athletic.