Zobrist's third-inning homer put Chicago ahead after center fielder Andrew McCutchen dropped Rizzo's two-out liner for an error.
With its seventh win in eight games, Chicago improved to a major league-best 20-6. The Cubs has won seven straight road games and completed their first sweep in Pittsburgh since Sept. 7-9, 2012. They lead second-place Pittsburgh by six games in the NL Central.
Lester (3-1) scattered eight hits in 5 2/3 scoreless innings, struck out five and walked two. The left-hander has allowed one run or none in five of six starts this season.
