On May 11, 2013 — Adam Wainwright of the Cardinals retires the first 13 batters in his start against the Rockies. Combined with Shelby Miller’s 27 straight outs to end yesterday’s game, the Cardinals tie a record for most consecutive outs by one team against another at 40; the Texas Rangers had also performed the feat on May 3-4, 1996. A one-out walk to Todd Helton in the 5th inning ends the streak, but Wainwright keeps the no-hitter going until the 7th and ends up with a two-hit shutout, 3 – 0.

Source:
Baseball Reference May 11