All the goals came in the second half as the Saddlers recorded their first win over the Alex in nine outings going back to 2001.
The result was also a first victory in six games for Smith's side and saw them keep only their second clean sheet of the season.
"It was a very good away day performance," said Smith. "I thought we controlled the ball possession-wise first half without being potent in the final third.
"The first half was more about possession than goalscoring chances. But in the second half the first goal was pivotal and once we got it I thought it gave us a lot more belief and know-how on the ball in the final third.
"The pressing when we won the penalty was fantastic. Craig Westcarr wins the first header, then Troy Hewitt and Ashley Hemmings are pressing. Westcarr then robs the lad and gets brought down - and he's scored his penalty.
"We're really pleased. It was a really professional performance and I was pleased with it."