Romero allowed a pair of Yankees runs in the top of the first inning before leaving after three frames due to an apparent leg injury with the Jays trailing 2-1.
Hill (1-0) came in and followed with a trio of scoreless innings to earn the victory.
Brad Lincoln, Aaron Loup and Steve Delabar combined for two more shutout frames and Casey Janssen secured the victory with his 21st save as Toronto took a 2-1 lead in the four-game series.
Adeiny Hechavarria's RBI double in the sixth inning drove in the go-ahead run while Rajai Davis homered and supplied a run-scoring single for the Blue Jays.
New York's Andy Pettitte (5-4) absorbed the loss, yielding three runs on five hits over 5 2/3 innings.