Trevor James Morgan's side now have four points from two games. For the Shivajians, veteran stopper Gourmangi Singh had equalised in the 64th minute after Wedson had converted a penalty in the 13th minute.
Plaza scored the winner, 10 minutes from final whistle.
The Shivajians started with aged players like Nirmal Chettri and Gouramangi while India internationals like Seityasen Singh and Sumeet Passi warmed the benches.
The referee promptly pointed towards the dreaded spot. The Haitian himself made no mistake in converting the spot kick much to Morgan's delight.
More From This Section
Wedson could have made it 2-0 but his powerful pile driver was saved by Poirei and he again did well to save an angular low shot.
The second half saw Shivajians introducing Milan Singh and Jerry Lalrinzuala for an off-colour Pradhan and Narzary.
While East Bengal were dominating, the equaliser came against the run of play. Spaniard Juan Quero Barreso's indirect free-kick landed perfectly for Korean Kim Song Young's headed effort, which was parried away by Rehenesh, but Gourmangi slotted home from the rebound.
A change in shape for the away team resulted in a well-crafted goal on the break through Willis Plaza. The Trinidad and Tobago international had a couple of good chances in the first-half but failed to capitalise. This time, Plaza made no error, putting his side 2-1 up in the 80th minute.