First-half goals from former Manchester United striker Febian Brandy and Paul Downing set Walsall on their way before James Baxendale made it 3-0 shortly after the break.
Bailey Wright scored little more than a consolation for Preston in injury time with North End now winless in three games and winless at home in the league in nine.
The Saddlers themselves were in a poor run of form before the turn of the year, failing to win in 16 between October 2 and December 15, and boss Smith believes they were unstoppable at Deepdale.
"I'm very happy. I'm pleased with the performance and pleased with the result," said Smith. "I thought we were really, really organised. Whoever we came up against, they would have found it hard to get through us. The two central midfielders were fantastic and the two centre-halves dealt with everything.
"To a man I thought we were excellent and very clinical in our finishing as well. It would have been nice to get a clean sheet but we came to get a win and that's what we've got.
"The upturn in form has been down to being consistent. We never changed our belief. We were having a poor run but it has just got better and better.
"We were consistent in our beliefs of what we wanted to do and how we wanted to do it. I was consistent with the players and they were consistent with me."
Meanwhile, Preston defender Wright admitted scoring did not help ease the depressing feeling that failing to win at home once again had caused.
"We're not happy. It's not nice. A performance like that, whether it's home or away, is not good enough," said Wright. "It wasn't a good afternoon for us as a team and we are not happy with it. It's got to be better."