After former Luton forward Scott Rendell had put the Cards ahead on four minute, Walls replied 60 seconds later with his first goal for the club.
He added another on the stroke of half time, before being replaced on 83 minutes.
Town midfielder Jim Stevenson was fouled by Jon Jones in the incident that saw the Woking player dismissed after half an hour, but carried on to complete the whole game, picking a yellow card in the process.
Midfielder Solomon Taiwo finally started his first game for Aldershot, completing a welcome 90 minutes, as they were held to a 2-2 draw at home by Forest Green.
Bedford's women cricketers make it three wins in a row
Setchell feels Bedford Town deserved their opening point at Stratford
Clubs all set for big kick-off as Bedford Town, Ampthill Town and Real Bedford begin campaigns
Industry gives way to housing
Blake claims victory in juniors Captain's Day at Bedford & County Golf Club
Winger Shaun Whalley was substituted after an hour as AFC Telford moved top of Skrill North with a 1-0 win at Worcester City.
Striker Jake Woolley netted as St Neots Town beat Arlesey Town 3-1 in their Calor Southern League Premier Divison clash.
The forward came off the bench on 64 minutes and was immediately into the action, scoring the Saints’ second goal seven minutes later.
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