Hillians off bottom after beating Tonbridge, Heath lose to Bridges
Ian Chapman's men made it six points in two games following their 2-0 win against Harlow Town midweek.
And Smith-Joseph's eighth minute strike was enough to see them leapfrog Tooting and Mitcham United in the Bostik Premier Division table.
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Hide AdThe Hillians are now just a point behind Harlow Town and Worthing, with games in hand.
Haywards Heath Town's lead at the top of the SCFL Premier was closed to two points after they lost 4-1 to Three Bridges. Jack Langford scored Heath's only goal.