At 39 straight batters is Randy Johnson in 2004. On May 12, 2004 Johnson gave up a single to Joe McEwing of the Mets to lead off the inning then retired the next three batters and three more in the seventh before being pinch hit for. In his next start, on May 18, 2004, Johnson threw a perfect game in Atlanta. On May 23, 2004 in Florida, Johnson retired the first six Marlins, but Abrham Nunez led off the third with a double to end the streak at 39.
At 40 straight batters is Tom Browning in 1988. On September 11, 1988 Browning gave up a one-out single to Rick Dempsey of the Dodgers in the fifth. Browning retired 11 straight Dodger hitters after that and was pinch hit for in the top of the ninth. John Franco would lose the game on a walkoff homer by Jeff Hamilton.
In Browning's next start, he faced the Dodgers again, but this time in Cincinnati on September 16, 1988 and Browning went through L.A. 27 straight.
Next up for Browning would the Giants at home on September 21, 1988. He got Brett Butler and Robby Thompson to start the game, but Will Clark singled with two outs, ending Browning's streak at 40 straight batters.
Jim Barr's record streak of 41 straight batters retired came in two games. On August 23, 1972, Barr walked Pirate pitcher Bob Moose to lead off the third and then the remaining 21 Pittsburgh hitters went down.
Then on August 29, 1972, Barr started for the Giants in St. Louis and retired the first 20 Cardinals hitters. But Bernie Carbo doubled with two outs in the seventh. The Cardinals would get just three hits in the game.
Jenks streak is stretched out over 13 games and he has not allowed a batter to reach since July 17.