The striker celebrated her return to the starting XI as the Reds fought hard to clinch back-to-back wins in the Women's Super League.
With the man who led the Reds to successive Super League titles Matt Beard in the opposite dugout for the Hammers, the away side made a fine start to the game by taking the lead on eight minutes.
A cross from Jess Clarke was half cleared and Sweetman-Kirk pounced to net from close range.
A second goal came close minutes later when Rhiannon Roberts fired an effort just wide, and Clarke was unfortunate to see her shot hit the side netting.