The hosts would have climbed into the top three with two games left had they beaten their promotion rivals.
But ex-Bury midfielder David Worrall came off the bench to break the deadlock with a 74th-minute free-kick and Southend hung on for a sixth straight win to go level on points with third-placed Wycombe.
Having made the match free entry, Bury were cheered on by their biggest home crowd in almost 18 years and bossed the first half.
Andrew Tutte and Nathan Cameron went close early on before Danny Mayor’s shot was deflected over.
Moments later Tom Soares headed wide from a Chris Hussey cross and Joe Riley curled a free-kick wide after the break.
But Southend then got a foothold in the game and Gary Deegan’s long-range strike stung the palms of Bury keeper Nick Pope.
And although Bury sub Danny Rose drew a straightforward save from Daniel Bentley, the Shrimpers took the lead moments later.
Kelvin Etuhu fouled Jack Payne 20 yards out and substitute Worrall curled it over the wall and into the top corner.
Bury pushed for an equaliser but Cameron headed wide from a Craig Jones cross before Bentley made a point-blank save to deny Ryan Lowe at the death.