In 1987, she broke the world records in the 400-meter, 800-meter, and 1,500-meter freestyle distances. At the 1988 Summer Olympics in Seoul, South Korea, she won three individual gold medals, and she also earned the nickname "Miss Perpetual Motion.".[9]

In these Olympics, Evans set a new world record in the 400-meter freestyle event. This record stood for 18 years until France's Laure Manaudou broke it in May 2006.

Evans held the 1,500-meter freestyle record, set in March 1988, through June 2007, when it was broken by American Kate Ziegler with her time of 15:42.54.

Evans held the world record in the 800-meter freestyle, 8:16:22, that she set in August 1989, until it was broken by Rebecca Adlington of Britain in August 2008. Adlington set the new record with her time of 8:14.10 in winning the race at the 2008 Summer Olympics. Evans's 800-meter record was one of the longest-standing ones ever in swimming, and it went unbroken through four Olympic Games (1992–2004). Only the 100-meter freestyle swimming record set by the Dutch swimmer Willy den Ouden stood longer—from 1936 through 1956, during a period when international competition was interrupted by world war.

Following her outstanding performance of 1988, Evans continued to dominate the world's long-distance swimming competitions (400 meters and above). Evans became the first woman to win back-to-back Olympic and world championship titles in any one swimming event by winning the 1988 and 1992 Olympic gold medals and the 1991 and 1994 world championships in the 800-meter freestyle race. She would astonishingly go undefeated in all of the 400-, 800-, and 1500-meter freestyle events for over five years, only being broken with her shock defeat by Dagmar Hase in the 400-meter freestyle at the Barcelona Olympics, where she led for almost the entire race but was narrowly caught at the end.

Evans won the 400-meter and 800-meter freestyle events at the U.S. National Championships 12 times each, the largest number of national titles in one event by an American swimmer in the 100-year history of the competition.

Evans ended her swimming career, for all practical purposes, at the 1996 Summer Olympics in Atlanta, Georgia. She did not win any medals, but she did add one more highlight to her life. She was given the honor of carrying the Olympic torch in the opening ceremony, and she handed the torch to the American boxing legend Muhammad Ali to light the cauldron. On July 27, 1996, she was in a building being interviewed by a German newsman when a bomb exploded nearby. The explosion very lightly shook the building and startled Evans.

In the swimming pool, Evans finished ninth in the preliminaries of the 400-meter freestyle. She did not qualify for the finals, as only the top eight finishers advance to the next level. In the final swim of her career, Evans finished in sixth place in the 800-meter freestyle.

At the Atlanta Games, American swimming officials criticized Ireland's Michelle Smith about her unexpected gold medals,[10] suggesting that she might have been using performance-enhancing drugs. When asked about the accusations, Evans said that when anyone like Smith showed such a significant improvement, "there's always that question." American sportswriters sympathetic to Smith took this comment to mean that Evans was accusing Smith of steroid use as well,[11] and they attacked Evans as being a sore loser. Evans later insisted that she meant no such accusation and that her remarks were taken out of context. In 1998, Smith received a four-year suspension for tampering with a urine sample.

At the end of Evans's swimming career, she held seven world records, five Olympic medals (including four gold medals), and 45 American national titles – third only to Tracy Caulkins and Michael Phelps.

In June 2011, it was reported that Evans was in the process of a comeback and had been training for six months with the goal of competing at the 2012 U.S. Olympic Trials.[12] At the 2012 Olympic Trials, at the age of 40, she ended up finishing 80th out of 113 swimmers in the 400-meter freestyle[13] and 53rd out of 65 swimmers in the 800-meter freestyle.[14]

Evans was inducted into the International Swimming Hall of Fame as an "Honor Swimmer" in 2001.[15]

Evans was serving as Vice Chair and Athletes director for the Los Angeles 2024 Olympic bid committee and was traveling with the team to promote Los Angeles as a candidate city.[16] Los Angeles was finally awarded the 2028 Summer Olympics at the 131st IOC Session in Lima, Peru, on September 13, 2017.[17]