The Bears, who backed up their opening-night league win against Leicester Tigers, had fallen 19-8 down during the first half, but they fought back to secure a maximum haul.
Second-half tries from Max Lahiff and Harry Thacker added to Magnus Bradbury’s first-half double.
And Lam said: "I am very proud of the team.
"Once again, the second week in a row, we played as a team.
"Saints came out firing, we had to repel them a couple of times and they scored a couple of good tries but there was a lot of guts from us, particularly when we were down to 14 men with Gabriel Ibitoye in the sin bin.
"We just kept them out and worked our way back into the game.
"The messaging from the players at half-time, and even after they scored out of nothing from the charge-down when we were attacking early in the second half, was all so calm.
"We did our jobs and we got out in front with a nine-point lead.
"In the end it was just pure guts and keeping to our systems.
"(Defence coach) Jordan Crane has put a lot of work defending from our try-line and they stuck to it and we got the bonus point win so I am very pleased."