Wanderers, last season’s champions when playing as Rushford Park, made a quick start before Bedians fought back.
The Premier Division fixture was played on Bedians’ grass pitch, which was in immaculate condition.
Wythenshawe Wanderers went two goals ahead early in the game with two well-taken finishes.
Bedians responded and had pulled level by half-time.
Both teams scored once more during the second half as the match finished 3-3.
Wanderers goalkeeper Leyton Entwistle was in superb form during the second half.
The result came as both clubs began their latest Premier Division campaigns, with Wanderers competing under their new name after winning last season’s title as Rushford Park.
Elsewhere in the division, Oldham Hulmeians won 5-3 at Chadderton Cott, while new side AR Elite moved top following a 3-2 victory at Manchester South End.
AFC Urmston Meadowside Redstar also made a strong start with an 8-0 win at Winton Wanderers.
