The hosts took the lead in the 50th minute when Febian Brandy was tripped by Danny Holmes and Will Grigg notched his 18th goal of the season with a low drive from the subsequent penalty.
Seven minutes later a fantastic 30-yard shot from Craig Westcarr increased the Saddlers' lead and Rovers rarely looked capable of saving a point.
"The lads have that spirit and work ethic in abundance," Smith said.
"Craig Westcarr scored a fantastic goal but you can also talk about Will Grigg scoring another penalty or two great blocks by James Chambers.
"It had to be a battle and we knew what to expect from Tranmere. The lads are comfortable and confident in their own ability and at times played some very good football."
Several npower Championship managers were at the game and Smith admitted that was to be expected for a young team doing well.
One target could be former Manchester United striker Brandy although he has indicated he wants to stay at the Banks's Stadium and may sign an extended contract.