It did not take long for Uruguay to open the scoring, with Giorgian de Arrascaeta thumping a free kick into the top corner after just four minutes.
New Zealand managed just the one attempt on target in the first period, as Ryan Thomas's effort from outside the box was comfortably gathered by the opposing goalkeeper.
Gimenez came close to adding Uruguay's second in the early stages of the second half, but once more his effort was wide of the target, with New Zealand somehow remaining in the match.
Nicolas Lopez was next to come close for the South American outfit just past the hour mark, but the Roma midfielder flashed his effort wide of the post.
Storm Roux remained New Zealand's main outlet in the second period, but it was Lopez who made sure of the points with a close-range finish late on.
Three points in Uruguay's final Group F match against Uzbekistan on Saturday would book their spot in the next round.