On September 5, 1963, Curt Flood's 5 for 5 day, along with a complete game effort by Curt Simmons highlighted a 9-0 beatdown of the Mets in St. Louis.
Flood's efforts included a triple, a ribbie, and two runs scored. Tim McCarver also tripled in the contest to open up a 5-0 lead in the seventh, then the Cardinals backstop capped off a four run eighth with a single, which was followed by Flood's fifth hit of the day. While the Cardinals offense was pounding New York's pitching, their batters had no answer for Simmons who scattered six hits, struck out seven, and did not walk a man.
The win had extended the Cardinals winning streak to eight straight, and they would win the next game as well to extend it to nine the next day. However, it was also snapped that next day, as the club dropped the second game of a doubleheader to the Pirates in Pittsburgh. At that point it was their longest winning streak of the season, as they made a late charge at the National League Pennant. After losing that second game in Pittsburgh the Cardinals rattled off 10 wins in a row. At the end of that streak they were trailing in the standing by one game.
Unfortunately the it all came apart right there at the end, as they lost 7 of their last 10, and ended up six games back in the standings. While that might have been the case, the Cardinals finished with a respectable 93-69 record. One year later the club finished with an identical record, but with a little help from the Phillies, and one great stretch of baseball they took the top prize in the National League, and they followed it up by taking the top prize in all of baseball.
Check out the box score here: http://www.baseball-reference.com/boxes/SLN/SLN196309050.shtml