Slough missed an early chance to take the lead when a poor corner from Luke Knight was missed at the near post and the ball rolled all the way along the six yard box, with no Slough player able to connect.
Smith gave Slough the lead on 21 minutes, finishing with aplomb after superb link-up play with Scott Harris, and doubled the lead on 42 minutes when he looped a header over Waders' keeper Tom Gowans. Before that, Knight had clipped the outside of a post with a strike from the edge of the box.
Slough played the ball around confidently, but lost influential winger James Dobson to an ankle injury in the first half. Guy Hollis replaced him, and Slough changed their shape with Hollis moving the right-back and Sean Fraser to the right side of midfield.
Biggleswade recovered strongly in the second, with substitutes Jordan Davis and Craig Daniel doing the damage.
Sam Ives poked the ball well wide after a quick break and cross from Conner Roberts, and Scott Harris saw a flicked effort saved by Gowans.
But on 59 minutes, Davis smashed a shot into the top corner to reduce the arrears, before Daniel equalised on 68 minutes with a cool finish amidst static defending.
Slough had the chances to regain the lead though, and Knight, after seeing his initial effort saved, sliced the rebound well wide on his left foot.
The goal of the game on 88 minutes looked to be the winning effort. Biggleswade broke quickly from a Slough corner, and Daniel raced the length of the pitch, evading several challenges as he went, before beating Aleks Gogic from the edge of the box to send the home support and coaching staff wild.
But in the second minute of time added on, Smith pounced to turn the ball home after a long throw fell to him at the back post, after his initial headed effort had hit the post, and the Rebels left the Carlsberg Stadium with a hard-fought point against Chris Nunn's depleted side.
Biggleswade Town Line up
Tom Gowans, Conner Roberts, Mark Coulson, Josh Beech, Stuart Farrell, Lee Allinson (c), Sam Ives, Ian Rees, Kelvin Bossman, Lee Reed, Zane Banton. Subs: Cameron Mawer, Jordan Davis, Craig Daniel, Kyal McNulty.