The former Kaizer Chiefs defender gave Sabah a route back into game after Serhou Guirassy had given the German side the lead in the 10th minute.
McCarthy leveled the contest six minutes before the halftime break, rising highest to head home his first goal in Europe’s elite club competition in what was his third appearance.
Guirassy would have the final say, however, as the Guinea forward scored what proved to be the winner in the 53rd minute as Dortmund took all three points.
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McCarthy also made a fantastic block to deny Guirassy a hat-trick strike, but the Azerbaijani champions did not have it in them to fight back for a second time.
In Tuesday’s other early kick-off, Slavia Prague recovered from 2-0 down to draw 2-2 at Fenerbahce, with Pavel Kacor netting late on.