After Marc Rzepczynski struck out Jay Bruce to start the 10th, Victor Marte (2-2) relieved and served up the decisive blast to Ludwick, who handed the Reds their fifth straight victory.
It was the third game-ending, walk-off homer of the year for Cincinnati, which came into the contest tied with Pittsburgh for first place in the National League West.
Sam LeCure (3-2) hurled a scoreless top of the 10th to earn the victory.
Bruce and Zack Cozart also provided RBI in the victory.
2014: The Year in Music [PHOTOS]