Story also became just the fifth major league player since 1900 to homer in each of his team's first four games to start a season, joining Chris Davis in 2013, Nelson Cruz in 2011, Mark McGwire in 1998 and Willie Mays in 1971.
Story has hit five home runs since making his debut on opening day. His latest shot was a two-run drive off San Diego right-hander Colin Rea in the fourth inning.
After hitting four homers in Arizona, Story made his debut Friday at hitter-friendly Coors Field, where the Rockies raised the height of the fences over the winter.
His 411-foot drive down the left field line was a no-doubter, though. It pulled the Rockies to 6-5 and chased Rea.
Story said Thursday he had donated his helmet at batting gloves from his historic start to the baseball Hall of Fame but wasn't about to part with any of his bats.
Story also had an RBI single in the second.
The Associated Press contributed to this report.