Southend began the day fifth, but have now leapfrogged their opponents thanks to Worrall's 25-yard free-kick 16 minutes from time.
Phil Brown's side are now behind Wycombe Wanderers on goal difference, while Bury are two points further back.
It was a disappointing result for the home faithful, which numbered more than 8,000 after Bury allowed free admission following the original fixture's abandonment back in March due to heavy rain.
Second-placed Preston overcame Notts County 3-1 at Meadow Lane, but MK Dons remain a point behind them following their 3-0 home success against Doncaster Rovers.
County's defeat leaves them two points from safety, level with Leyton Orient, who lost 1-0 at Rochdale.
Swindon Town's hopes of automatic promotion are effectively over after they were held 3-3 at home by Walsall, while elsewhere Scunthorpe United drew 1-1 with Bradford City.
