Professional career
Because of his lack of playing time at UCLA, few NBA teams had an interest in Eaton after he finished his college career. He paid for two tryout camps, but only received an offer of $15,000 to play in Israel and another for $25,000 in Monte Carlo. However, the Utah Jazz, who finished in last place the prior season, saw him as a potentially dominant defender and selected him as a long-term project in the fourth round of the 1982 NBA draft with the 72nd overall pick. Utah coach Frank Layden quipped, "Like [former University of Utah coach] Jack Gardner said, 'You can't teach height.'" Also the team's general manager, Layden discouraged Eaton from playing in Europe and signed him to a five-year contract, with the first season guaranteed at $45,000, for a total $570,000.
Eaton had worn No. 35 at UCLA, but the number was already taken on the Jazz by Darrell Griffith, prompting Eaton to choose the reversed No. 53. Entering the NBA, Eaton's goal was to become a journeyman backup. He made an immediate impact as a rookie, starting 32 games and replacing Danny Schayes after the cash-strapped Jazz traded the center mid-season. Eaton finished the season with a then-franchise record 275 blocked shots while averaging only 19 minutes per game. His 3.4 blocks per game ranked third in the NBA, behind Atlanta's Tree Rollins and San Diego's Bill Walton.
The Jazz placed Eaton on a six-day-a-week program in the offseason. Layden said they treated him "like a high school kid as far as basketball skills are concerned". Eaton continued to improve in his second season. In 82 games in 1983–84, he grabbed a team-leading 595 rebounds and blocked 351 shots (breaking his own franchise record). His 4.28 blocks per game led the NBA, well ahead of Rollins (who finished second with 3.60 blocks per game). During the season, he failed in his attempt to block the skyhook which gave Kareem Abdul-Jabbar his 31,421st point to break the NBA career scoring record held by Chamberlain. Eaton's strong defense helped the Jazz improve from 30 to 52 in his rookie season to 45–37, winning their first Midwest Division title and making their first playoff appearance.
In Eaton's third season in 1984–85, he blocked 456 shots, shattering the NBA record for most blocked shots in a single season set during the 1973–74 season by Elmore Smith, who had blocked 393 shots for the Los Angeles Lakers. Eaton averaged 5.56 blocks per game, an NBA single-season record that was more than double the league's second-ranked shot-blocker that season (Houston's Hakeem Olajuwon with 2.68 blocks per game). In addition, Eaton averaged 11.3 rebounds per game, ranking fifth in the league in that category. "We had no idea that he would develop the way he has," said Layden during the season. Eaton was not on the All-Star ballot that year after being one of the final cuts. For his efforts, he was named to the NBA All-Defensive First Team and was honored as the NBA Defensive Player of the Year. On April 26, 1985, Eaton set an NBA single-game playoff record with 10 blocks in a 96–94 loss to the Rockets. His mark stood until 2026, when Victor Wembanyama had 12.
Although he was not a significant offensive contributor, the Jazz relied heavily on Eaton for his shot-blocking, rebounding, and occasional "tippy toe" dunks. With the emergence of superstars Karl Malone and John Stockton, the Jazz became one of the best teams in the NBA. Eaton's stifling defense was a major factor in Utah's success. He continued to rank among NBA leaders in blocked shots, leading the league in 1986–87 and 1987–88. On November 17, 1987, Eaton set a career high with 25 rebounds in a 120–110 win over the Denver Nuggets. In 1988–89, he averaged 10.3 rebounds per game (seventh in the NBA) and 3.84 blocks per game (second behind Golden State's Manute Bol). He was named NBA Defensive Player of the Year for the second time in his career and received his third selection to the NBA All-Defensive First Team. In addition, he was chosen to play in the 1989 NBA All-Star Game, joining teammates Malone and Stockton on the Western Conference team. It was the first time that the Jazz had three players in the All-Star Game.
In the 1989 playoffs, the second-seeded Jazz were upset in the first round 3–0 by the seventh-seeded Warriors. Golden State coach Don Nelson spread out his offense and avoided going inside against Eaton, and they played most of the series with a small lineup in which their tallest players on the court were 6 ft 8 in (2.03 m) Larry Smith or Ben McDonald or even 6 ft 7 in (2.01 m) Rod Higgins. Opponents were increasingly playing with smaller lineups, forcing Eaton to guard a quicker player who would draw him out to the perimeter and seek to drive past him. Utah coach Jerry Sloan countered by decreasing Eaton's playing time and employing his own small lineup with backup center Mike Brown. In 1991–92, there was speculation that the more offensive-minded Brown would start the season at center, but Sloan stuck with Eaton. However, Eaton's playing time dropped to 25 minutes per game from 32 minutes in 1990–91.
After missing just nine games in his first 10 seasons, Eaton was hindered by knee and back injuries late in his career. His rebounding and shot-blocking averages declined. During the 1992–93 season, knee surgery and back problems limited him to 64 games, averaging 17.3 minutes per game, both career lows. A degenerative back ailment forced him to drop out of training camp and miss the 1993–94 season; his contract expired at the end of the season. After therapy failed to correct the problem, he announced his retirement from basketball in September 1994.