Jenks had an opportunity to pass Jim Barr, who set the record with the 1972 San Francisco Giants, but Joey Gathright knocked an opposite-field base hit to lead off the ninth inning, ending a streak dating back to July 17.
Gathright battled the hard-throwing Jenks, fouling off four pitches before slapping the sixth pitch of the at-bat between shortstop Juan Uribe and third baseman Josh Fields. It was a dramatic at-bat, with flashbulbs firing around U.S. Cellular Field with each pitch.
Gathright nearly ended the streak earlier in the at-bat, when he scorched a line drive that landed just foul down the left-field line.
"It was outstanding to watch what he did," White Sox manager Ozzie Guillen said. "Obviously, everything comes to an end, unfortunately. Everybody in baseball should be bummed out about his, but that happens. It was a nice ride. It was enjoyable, especially with the kind of year we've had. This year, having something like that happen is good to see. It can't happen to a better kid."
It was Jenks' first trip to the mound since he tied the record on Aug. 12, but he said the time off did not affect him.
"I felt fresh," Jenks said. "I was throwing bullpens during the road trip, so I was feeling good. I was fresh and ready to go."
Jenks looked frustrated, but still calm, as he came back and finished off the next three hitters in order to seal the win, snapping an eight-game White Sox losing streak.
"There was relief," Jenks said. "I was so amped up facing him that I got out of control a little bit. Putting him on base and then getting that first out calmed me down. I was able to make every pitch after that."
Jenks had refused to talk to the media since the streak had approached the previous American League record of 38, which had been held by David Wells. But he sat down for a lengthy and relaxed session with the press after Monday's game.
"I can sit here and talk to you fine people again," Jenks said. "I am sharing a record that is still something special and might not happen for me or somebody else for a long time, so I'm real happy with it."
As for what's up next for the White Sox closer, he says for now it is three down, 38 more to go.
"This is how it started in the first place," Jenks said. "Let's just keep it going from here."
Alex Gyr is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.