The Southern Section final seemed to be heading to penalties with the O's leading 2-1 on the night with 90 minutes on the clock.
However, Reeves had other ideas and, after being teed-up by a low, left-wing cross from Kevan Hurst, the on-loan Southampton midfielder guided the ball into the back of the net from six yards.
The Shrimpers had taken a 1-0 lead into the second leg after grinding out a hard-fought win at Brisbane Road.
But Orient wiped that narrow advantage out after just eight minutes when Dean Cox's low right-wing cross picked out Shaun Batt who nipped in ahead of the returning Mark Phillips and steered home a low volley from eight yards.
Substitute Barry Corr volleyed the Shrimpers level in the 61st minute but Orient hit back with David Mooney heading home before Reeves' late shot handed Southend their first Wembley appearance in 83 years.