The frontman bagged the only goal of the game just seven minutes after coming off the bench. And the match-winning effort was also enough to push the Shrimpers back in to the League Two play-off positions.
Up until then it had been a frustrating afternoon for Phil Brown's side who had been able to make a breakthrough.
Centre-back Jakub Sokolik missed the Shrimpers' best chance in the first half when he volleyed over an open goal from just six yards out.
After the break, Southend skipper John White headed a Kevan Hurst corner against the crossbar and Lee Barnard fired just wide from 20 yards.
But, with 18 minutes remaining, Eastwood popped up to bag the game's winning goal as loanee Jacob Murphy's left-wing cross fell perfectly in to his path and enabled the striker to fire in to the roof of the net from six yards.