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Moments later Ben Coker tested the veteran Stevenage goalkeeper with a curling shot, but it came to nothing as the 39-year-old dived low to his left to gather.
Neither side could break the deadlock come the half-time whistle, although Corr had a great chance just before the break when he lofted the ball over Day, but the effort floated wide.
Stevenage went on to break the deadlock five minutes before the break when Dean Parrett's free kick on the edge of the box took a deflection into the path of Tom Pett, who slotted home past Daniel Bentley from six yards out.
It didn't take long for Southend to equalise, however, as a prolonged period of pressure culminated in Stephen McLaughlin's cross falling for Ryan Leonard at the far post, and the 22-year-old made no mistake from close range.
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There was late drama as the hosts came within a kick of winning the game when Leonard went down in the box under pressure from Parrett in the sixth minute of injury time, prompting referee Graham Scott to point to the spot.
It wasn't to be, however, as Corr's chip down the middle ended up clipping the bar and going out of play to take the game to extra time.
Determined not to rue their missed opportunity from the spot, the Shrimpers set about trying to edge themselves in front and only had to wait until the 108th minute when McLaughlin smashed a bullet header past Day.
A tense period followed for Southend, but the game was ultimately put to bed right at the death courtesy of Michael Timlin, who curled a third from the edge of the box to see the hosts through to the final 4-2 on aggregate, much to the delight of the home fans who went on to invade the Roots Hall pitch.