The 6ft 10in forward/centre came off the bench to inspire the Magic to their third victory of the NBA campaign, which began a week ago. Orlando were struggling until Amaechi, who was brought on for the centre Michael Doleac, made two free throws.
"We started slow, but I told our guys if we just keep the pressure on, it will turn our way," the Magic coach Doc Rivers said. "We make so many substitutions that we knew we could find a way to give us the break we needed."
Amaechi, who led Sheffield Sharks to a Uni-ball Trophy when he played in England, struggled from the field, making only five of 14 shots. He did most of his damage by pounding away inside and getting to the line, where he scored with eight of nine his free throws. He also sealed the victory with a crucial basket in the final stages of the contest.
Darrell Armstrong had given the Magic a 95-94 lead with a driving lay- up in the final two minutes before Amaechi struck the killer blow by hitting from four feet and drawing a foul. He converted the three-point free throw.
Orlando are now one game behind the Atlantic Division leaders, the New York Knicks, who are hoping to reach the NBA finals for the second season in a row.