Smith capitalised on a defensive mis-judgement just short of the hour-mark, but the Hornets' victory was more comfortable than the scoreline suggests, albeit against a Charlton side who were forced to play the second 45 minutes with ten men.
Both sides could have taken the lead inside the first three minutes of the game.
First Hameur Bouazza struck a 25-yard rising drive narrowly over Mart Poom's bar and then Smith's centre from the left side of the area picked out Jobi McAnuff, who headed back and beyond Weaver only to see Mark Hudson clear off the line.
But the manner in which the home side took the lead in the 28th minute was rather ironic considering their new style of play.
A long clearance from Poom was badly misjudged by Jonathan Fortune, giving Smith a clear run on goal and the forward calmly slid the ball beyond Weaver to net his first of the season.
Watford were the better side throughout the first half but they were handed an unexpected bonus on the stroke of half-time when referee Iain Williamson rather harshly adjudged that Kelly Youga had fouled Tamas Priskin on the edge of the area.
Then having made that decision, Williamson had no option but to show the left-back the red card as he was the last man.
A couple of long-range efforts and a Luke Varney chance that was well smothered by Poom was all that Charlton could muster after the interval.
Watford were forced to settle for just the one goal, but they could and perhaps should have scored more.
Several opportunities were either blocked or the decisive final touch could not be applied when it mattered, while Weaver pulled off a terrific double save to deny McAnuff and Damien Francis.