The veteran striker, 35, bagged in the 3-1 win at Atherton Collieries, where he started up front alongside fellow veteran, 43-year-old Lee Hughes.
Hughes also got on the scoresheet, with Mason Warren giving Sports a 3-0 lead by half time.
Beavon has played more than 300 games in the Football League for the likes of Wycombe Wanders, Preston North End, Burton Albion and Coventry City.
He was most recently with Nuneaton Borough, who he joined in the summer. He moves to Sports on a season-long loan.
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