Ludwick's homer and a solo shot from Zack Cozart had given the Reds a 3-2 lead in the first inning, but the Padres took a 4-3 lead in the fourth, when Chase Headley drove in Alexi Amarista with a two-out single and Will Venable followed with a single that drove in Kip Wells.
The National League Central-leading Reds rallied off San Diego starter Kip Wells (2-4), with Drew Stubbs collecting a one-out single and then scoring the tying run -- and chasing Wells -- when Jay Bruce doubled.
Dale Thayer entered the game, and Ludwick greeted him with a single to score Bruce, handing Cincinnati the lead for good.
Bronson Arroyo (7-6) allowed four runs on seven hits over six innings to earn the victory.
Wells was touched for five runs after coughing up four walks and five hits over 4 1/3 frames.
Chase Headley belted a two-run homer and finished with three RBI for the Padres.
Notable deaths of 2014 [PHOTOS]