The tricky winger dispatched from 12 yards after Sam Surridge was knocked over just inside the area to seal the Glovers’ place in Monday night’s draw.
Surridge, fresh from scoring twice in his last home outing, led the line for Darren Way’s side while fellow strikers Olufela Olomola and Francois Zoko served the first of their three-game suspensions.
Rhys Browne and Jake Gray replaced the duo as Town lined-up in a 4-3-3 formation.
The opening 15 minutes offered little in terms of chances but the hosts began brightly and a Nathan Smith attempt hit Gray, forcing Mark Oxley into a fine stop with Browne being denied by the offside flag on the follow up.
The two additions to the Glovers XI combined moments later. Gray’s defence-splitting pass was collected by an onrushing Browne, whose powerful effort blocked before Southend scrambled clear.
Anthony Wordsworth sent a warning shot at Artur Krysiak from 25 yards and Simon Cox had a similar effort which the Polish stopper needed to tip over.
Yeovil had a penalty appeal waved away by referee Craig Hicks when Anton Ferdinand collided with Surridge but the next time the AFC Bournemouth forward was bundled to the floor in the box, the Surrey-based official pointed to the spot.
A beautiful passage of play involving Krysiak, James Bailey and Bevis Mugabi saw the latter bomb down the right and find Surridge in the box.
When he was fouled by Jason Demetriou, Khan stepped to take the resulting penalty and converted low to the keeper’s left to take his seasonal tally to seven goals.
Experienced ex-Celtic man Marc-Antoine Fortune fired a daisy-cutter at Krysiak and Michael Kightly curled a free kick off target in rare visiting attacks as Town deservedly went into the break a goal to the good.
They nearly made it two on 47 minutes through a Gray strike which faded just past Oxley’s left-hand post before Josh Wright headed narrowly wide at the other end.
Both goalkeepers pulled off brilliant saves soon after, Oxley flying to stop Mugabi’s thumping nod while Krysiak saved expertly from Simon Cox and Demetriou.
Tom James’ knuckleball-style free kicks are becoming a bit of habit of late, and the left-back went close with a 25-yarder, which half of the crowd thought had nestled in the top corner.
An excellent slide-rule pass from Gray released Surridge for Town’s opportunity but the 19-year-old had his close range effort blocked.
Then Southend had their first attempt for a while with substitute Stephen McLaughlin seeing his piledriver cleared off the line by James.
McLaughlin again had an effort hacked away from James as the Shrimpers pushed hard for an equaliser and they did have the ball in the back of the net, although a blue shirt was alleged to have nudged Krysiak.
Holding firm defensively, Yeovil went on the hunt for a crucial second and a sublime sequence of one-touch passing saw Browne drag a shot wide but another goal wasn’t needed as the home side had already done enough to ensure progression to the next round.
Yeovil Town: Krysiak, Mugabi, Sowunmi, N.Smith, James, Gray (Santos 83), Worthington, Bailey, Khan, Surridge, Browne.
Bookings: Bailey 66, Mugabi 80.
Not used: Scott, Davies, Nelson, Dickson, C.Smith.
Southend United: Oxley, Demetriou, White, Ferdinand, Timlin, Leonard, Wright (McGlashan 77), Wordsworth (McLaughlin 54), Kightly, Cox, Fortune (Ranger 51).
Bookings: Kightly 41.
Not used: Bishop, Turner, Yearwood, Robinson.