In 1981, Moffet set a national high school record of 55.24 in the 100 metres breaststroke and finished fourth in that event at the national championships, also taking bronze in the 200 metres breaststroke. The following year, he won bronze medals in both of those events at the 1982 World Aquatics Championships and began attending Stanford University. He also swam in the heats of the gold medal-winning 4×100 metres medley relay. He set a Pan American Games record in the qualifying rounds of the 100 metres breaststroke at the 1983 edition, but ultimately finished second to his compatriot Steve Lundquist. He competed in that event at the 1984 Summer Olympics and set an Olympic record of 1:02.16 in the heats, despite injuring his thigh muscle during the race. This injury led him to finish fifth in the final and not start in the 200 metres breaststroke, in which he was also entered. That same year, he won those events at the National Collegiate Athletic Association (NCAA) Championships and held the world record in the 100 metres breaststroke from June 25 until July 29.