Craig Westcarr put Walsall in front after only two minutes, driving in a cross from Adam Chambers, and Slovakia Under-21 international Miklan Lalkovic, making his debut on loan from Chelsea, drilled home the second in the 25th minute.
Rovers skipper Andy Robinson pulled one back with a superb free-kick five minutes from half-time, but the Saddlers made sure of the points with a four-man move ending with Westcarr clipping home the clinching third goal.
Saddlers boss Smith said: "It's a really good start, but we lost our way a bit in the second half, though you have to give credit to Tranmere for the way they changed their system to cope with us.
"We have players with pace who can score goals, and I thought Westcarr and Ashley Hemmings were outstanding.
"It's a good start, but I won't say further than that. There is a long way to go. There were a lot of really good performances out there today, but we can get better.
"We always knew Tranmere would be a threat from set pieces, and we gave away too many cheap free-kicks and corners.
"Our third goal came from one of our best passing moves of the game, but up until then we had not been keeping the ball as well as we can.
"We should have had more than two goals in the first half when we had 16 attempts at goal and we got into some really good positions."
- Sports & Recreation
- Craig Westcarr
- Adam Chambers