Cameron Maybin and Chris Denorfia also homered off Cubs starter James Russell (1-3) as the Padres rebounded from a 2-1 loss in 11 innings in the afternoon opener. The teams were forced to play the doubleheader after Tuesday night's game was rained out.
After losing in Game 1 on Reed Johnson's homer, San Diego took the lead for good in the second inning of the nightcap on Ludwick's two-run shot. Maybin extended the lead to 3-0 with his homer in the fourth, and Denorfia connected on a solo home run in the fifth.
Johnson drove home Alfonso Soriano in the fifth for Chicago, and Soriano added a two-run homer in the eighth inning, but it wasn't enough to come all the way back.
Aaron Harang (4-0) gave up two runs over six innings before turning it over to the bullpen. Chad Qualls gave up Soriano's homer, which got Chicago within 5-4, but Heath Bell worked around a two-out single by Kosuke Fukudome in the ninth inning for his fifth save.
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The opening game of the doubleheader also came down to the wire.
The Cubs led 1-0 when starting pitcher Matt Garza left after six innings. He scattered six hits and walked three while striking out nine -- and even scored the Cubs' first run, on a single by Marlon Byrd in the third inning.
The Padres tied the game in the ninth against Carlos Marmol, when Maybin walked, stole second, went to third on Will Venable's bunt single and scored on Josh Barlett's sacrifice fly.
Johnson connected in the 11th off Luke Gregerson (0-1), the fifth Padres pitcher, for the game-winning homer. Reliever Jeff Samardzija (1-0) worked two innings for the victory.
Chicago could have prevented Game 1 from being so tight, squandering a chance in the third inning. After Garza scored, the Cubs loaded the bases with two outs. Carlos Pena grounded out to end the inning, leaving the Cubs clinging to a 1-0 lead.
The Padres threatened in the sixth when Garza walked the bases loaded with one out, but he escaped the jam by getting Brad Hawpe to ground into an inning-ending double play.
Quade pulled Garza after six innings and employed three relief pitchers in the seventh to prevent the Padres from scoring. Left-hander Sean Marshall walked Orlando Hudson to load the bases with two outs before getting Headley to ground out with a full count.
After the Padres tied it in the ninth, Mike Adams gave up a two-out single to Fukudome, ending a streak of 28 consecutive batters retired.
San Diego loaded the bases with one out in the 11th, but Headley and Hundley each flied out to end the threat.
Fukudome was out of the Game 1 starting lineup, but the outfielder entered the game in the seventh in right field. His wife delivered a baby girl, the couple's second child, on Tuesday in Chicago ... Tuesday's rainout was the first of the season for either team. Conditions on Wednesday were overcast and dry with temperatures in the 40s. ... With a Thursday home game with Philadelphia, the Padres planned a quick departure from Chicago.