The Welshman, who was celebrating his 24th birthday, scored with a gem of a left-foot volley after pulling down a pass from Gylfi Sigurdsson in just the 15th minute.
Tottenham made 10 changes at half-time, with Bale amongst those departing, and League One outfit Swindon earned themselves a draw as Andy Williams' strike took a huge deflection off Steven Caulker in the 76th minute.
Tottenham will now travel to Hong Kong on Sunday for the Barclays Asia Trophy tournament.
Newcastle started their pre-season campaign with a 4-2 win over Motherwell in Scotland.
Over 1,000 members of the Toon Army travelled to the match and they seemed to protest against owner Mike Ashley when they unfurled a large banner saying: "Support the team not the regime."
The only other Premier League team in action was West Ham who enjoyed a 2-1 win away at Colchester United.
Joe Cole put the Hammers in front after only seven minutes and Jason Collins made it two in the 51st minute. Jabo Ibehre got a last-gasp consolation for the League One side.
Elsewhere, a strong Galatasaray side needed a last minute winner from substitute Wesley Sneijder to secure a 2-1 win at Meadow Lane against English League One outfit Notts County.
A Dany Nounkeu own goal had given County an unlikely lead and it was not until the 80th minute that Burak Yilmaz equalised for the Turkish giants. Sneijder and Didier Drogba both played the entire second-half of the match.