Paul Sturrock's League Two promotion-chasers never looked out of their depth against their League One opponents, despite going behind to a 32nd-minute Matt Doherty penalty.
Referee Andy Haines had no choice but to point to the spot after both Bury strikers, Lenell John-lewis and then Troy Hewitt, were barged over in the box as they attempted to head home David Worrall's cross.
But Gavin Tomlin got Southend back in the tie with a mazy run and finish four minutes before the break, going to the byline and jinking past two Bury defenders before firing past Shakers goalkeeper Trevor Carson at his near post.
The Shrimpers' goal threat waned a little in the second half as Kevin Blackwell's men started to show their class, Hewitt going closest with an acrobatic volley that Southend goalkeeper Paul Smith just tipped around the post.
But Southend should have booked their place in the third round in stoppage-time when Michael Timlin hit the crossbar and substitute Barry Corr fired the rebound against the post with the Bury goal at his mercy.