The record for most hits by one team while being shut out is 14, set once in the NL and once in the AL. On September 14, 1913, Chicago Cubs ace Larry Cheney threw a complete-game shutout against New York, despite being beaten up by the Giant hitters. The Giants had a hit in every inning, but had only one runner reach third base. Cheney was helped by three New Yorkers getting caught stealing and one being thrown out trying to stretch a single into a double.
The Giants’ dubious record was matched on July 10, 1928 by the Cleveland Indians, who somehow could not score against journeyman Washington pitcher Milt Gaston. Gaston, who two years earlier had allowed 12 hits while shutting out the Red Sox, survived six leadoff hits and five Indians reaching third base.