It was the first 9-3-2-6-2-5 triple play in major league history, according to ESPN Stats & Information research.
"Besides marrying my wife and the birth of my kid, that's high up there," right fielder Adam Eaton said, smiling. "I've never had that much fun on a ballfield."
With the bases loaded and no outs, Eaton made a running catch of Mitch Moreland's drive down the line as the runners took off.
"[Moreland] hit the hell out of it, and I thought it was getting down and I broke," Fielder said. "Once I broke, there was no way I can get back and go, so I just messed it up."
Abreu raced to the clubhouse to watch the replay after the game.
"What a rush," starter Jose Quintana said. "I was yelling, 'Throw the ball to second.' It was fun. I've never seen that before."
It was the first triple play for the White Sox since Sept. 18, 2006, against Detroit. Texas hadn't been the victim of a triple play since June 1, 1991, against Seattle.
It was the first triple play in the majors this season.
The Associated Press contributed to this report.