Midfielder Mattis settled the issue with his first goal for the club a minute before the interval by expertly heading in a fine free-kick from substitute Chris Palmer.
The Saddlers were left with it all to do after Weston and Sansara were both dismissed with straight red cards.
Weston received his marching orders for a two-footed challenge on Dean Cox before defender Sansara was dismissed for bringing down Gary Hart.
The Seagulls - yet to win at home in the league this season - pushed Walsall back after the break but the Saddlers defended stoutly and keeper Clayton Ince made a series of important saves.
Ince's best save came soon after the interval when, from a cross by Hart, he tipped over Glenn Murray's firm header.