It took the Saints until first-half stoppage-time to break the deadlock, as Lambert squared for Jay Rodriguez to bundle home, but the hosts dominated throughout and could have had the game wrapped up by the interval.
They certainly did by the final whistle, with Lambert, Adam Lallana and Rodriguez again finding the target during a clinical second-half performance.
After seeing Southampton's England contingent do the business on the south coast, Lambert admitted afterwards that Mauricio Pochettino's side could not have done much more.
He told Sky Sports: "I think that's probably our best performance this season. We can't stop smiling. I think everyone agrees today that, to a man, we were superb. It was a great performance.
"I don't think there was anything different about today, it was just that we hit it off straight away.
"It was a little bit panicky because we had five or six chances that we didn't take, so we were a little bit worried, but we knew that we would get one and when we got that we should be able to play our football. I thought we were superb.
"We know that we're capable of that, we see it every day in training with the players that we've got. It's a pleasure to play with them day in, day out and it's good to get the rewards."
Lambert was also pleased to see the Saints offer the perfect response to last weekend's dramatic 3-2 defeat at Tottenham Hotspur.
He added: "We were disappointed but it's a hard place to go. We were desperate to bounce back and what a performance by the boys."