Wanderers took the lead through Nenad Milijas' first-half penalty after Sam Winnall was fouled by Chris Barker.
Shrimpers captain Craig Easton pulled back a deserved equaliser for the npower League Two outfit in the 80th minute, but Stearman had the final say deep into stoppage time at the end of the additional periods.
Wolves boss Mick McCarthy made 10 adjustments to the team which drew 1-1 at Everton in the Premier League on Saturday, with teenagers Winnall and Danny Batth handed their senior debuts for the Black Country club, Ashley Hemmings given his first start and Stearman named as captain.
Southend settled more quickly in a scrappy opening and had the first attempt on goal after 10 minutes, with Easton sending a volley over the bar.
Moments later Anthony Grant dispossessed Adlene Guediora and won a free-kick in a useful-looking position, but Sofiene Zaaboub swung it wide of the target.
At the other end, a scramble in the box ended with Greg Halford hitting an acrobatic effort which did little to trouble Shrimpers goalkeeper Glenn Morris.
The visitors were then awarded another free-kick just outside the area which was laid off to Grant, but the midfielder's low strike was deflected over.
Wolves had offered little, but all of a sudden found themselves a goal up thanks to a surging run from Winnall.
The 19-year-old broke into the box in the 27th minute and stepped over the ball several times before being brought down by Barker.
Referee Colin Webster pointed to the spot and Milijas stepped up to convert the penalty, rifling it powerfully to Morris' right.
Southend almost found an instant response, but Bilel Mohsni headed wide from Peter Gilbert's free-kick when he really should have hit the target.
The Tunisian had the ball in the net soon after only to be waved offside, before Sean Clohessy hit a weak effort that Wayne Hennessey collected comfortably.
Halford's long throw caused some problems in the Shrimpers area just before the break, but Morris dived on the ball.
Southend looked to pick up where they had left off as the second half got under way and Barry Corr twisted and turned in the box before unleashing a shot that Hennessey got down to save.
But Wolves came back strongly with a succession of attempts on goal, first from Winnall and then Hemmings.
Milijas was next up, hitting a hopeful effort high and wide, before Winnall connected well with Hemmings' cross but could not guide the ball on target.
Ronald Zubar then had a shot saved by Morris, but Southend were not out of the game and Blair Sturrock, son of the manager Paul, gave a reminder of that with a little under 20 minutes remaining by firing an attempt against the crossbar.
McCarthy made a double substitution in the 70th minute in an attempt to finish the job off, bringing on Sylvan Ebanks-Blake, who had netted against Everton, and last season's top-scorer Kevin Doyle for Hemmings and Winnall respectively.
But with 10 minutes to go, Southend snatched an equaliser as Easton stooped low to head Josh Simpson's cross past Hennessey.
Ebanks-Blake slotted home a close-range effort two minutes later, only to see the referee's assistant raise his flag to rule the strike out.
Having survived that scare, the Shrimpers sensed the opportunity to pull off a shock and play moved back into the Wolves half, but Mohsni was unable to keep his header down from a corner and Webster blew the whistle to confirm the need for extra-time.
The hosts had the better of the first additional period and looked to have regained the lead when Ebanks-Blake tapped the ball in after Milijas' shot had deflected on to the post, but again the striker was denied by the flag for offside.
Simpson blew a great chance to win it for Southend with seconds remaining, lifting a shot into the arms of Hennessey after substitute Louis Soares had squared it to him.
And it proved to be costly, as moments later Stearman bundled Zubar's cross over the line to give Wolves a last-gasp victory.