The early minutes saw few chances at either end, with neither goalkeeper extended.
The Shrimpers, who had already been to the Millennium Stadium this season for the LDV Vans Trophy final, struggled to make their mark against a rugged Red Imps backline.
Eighteen minutes in Jupp almost played in Mark Bentley, but Jamie McCombe was on hand to clear the dangerous cross from the right.
As the half-hour mark approached Bentley became the first player booked, but he then rescued his side by clearing from near his own goal-line after Darryl Flahavan failed to deal with a long throw.
Simon Yeo and Richard Butcher were thwarted when well placed, with Adam Barrett making an excellent double block for Southend nine minutes before the break.
After the restart, Francis Green's shot was straight at Flahavan from distance, before Wayne Gray set up Eastwood at the other end, but his shot was deflected wide.
Ten minutes in Eastwood fluffed his shot after a melee on the edge of the City area.
Just after the hour, Bentley's curling 25-yarder brought a save from Marriott, following good work by the impressive Eastwood.
Twenty minutes from time Che Wilson was in the right place to clear after another long throw led to Green capitalising on Flahavan spilling the ball.
Flahavan then redeemed himself with an excellent tip away as Yeo closed in on Green's overhead effort to the far post.
Bentley thought he should have had a penalty right at the death, but extra-time was needed to try and separate the two teams.
The first period of 15 minutes extra followed the pattern of the 90 beforehand, before Eastwood broke the deadlock in stoppage time - rifling the ball home from close in after a near-post corner had been blocked on the line by Matt Bloomer.
In the second half of extra-time the Imps threw everyone forward and were caught on the break as Eastwood raced clear and played in Jupp, who made sure of promotion with his first goal for the club.