The St. Louis Cardinals selected Gomber in the fourth round of the 2014 MLB draft and signed him with a $374,100 bonus. His first assignment was to the State College Spikes of the Class A-Short SeasonNew York–Penn League, where he recorded a 2-2 record and 2.30 ERA with 36 strikeouts in 11 games started for State College. In 2015, Gomber pitched for the Peoria Chiefs, where he was named a Midwest LeagueAll-Star. He finished the season with a 15−3 record and a 2.67 ERA, leading the league in wins, strikeouts and batting average against. At one point during the season, he won 13 consecutive decisions. The Cardinals named Gomber their Minor LeaguePitcher of the Month for August 2015, and, along with Alex Reyes, their Co-Minor League Pitchers of the Year. The Cardinals invited him to spring training as a non-roster player in 2016. Gomber began 2016 with the Palm Beach Cardinals and was promoted to the Springfield Cardinals in July. In his second start for Springfield on July 30, 2016, he pitched seven innings against the Northwest Arkansas Naturals and allowed one hit, no runs, two walks and struck out three. Gomber had started 19 games over Classes A-Advanced and AA to that point in 2016, allowing a 2.69 ERA and a 1.04 WHIP over innings. He finished the 2016 season with a combined 7-8 record and a 2.69 ERA in 21 starts. After the season, the Cardinals assigned Gomber to the Glendale Desert Dogs of the Arizona Fall League. Gomber was one of the best pitchers in the AFL and finished the season with seven games started, a 5-1 record, and a 2.14 ERA. Gomber spent 2017 with Springfield. After struggling during the first half of the season, Gomber posted a 1.92 ERA in his last ten games with Springfield. He finished the 2017 season 10-7 with a 3.34 ERA and 1.17 WHIP in 26 starts. The Cardinals added him to their 40-man roster after the season to protect him from being chosen in the Rule 5 Draft. Gomber began 2018 with the Memphis Redbirds. On April 23, 2018, in a game against the Iowa Cubs, Gomber tied the Redbirds' franchise record for strikeouts in a game with 16, joining Lance Lynn who also struck out 16 in 2010.
Major leagues
The Cardinals promoted Gomber from Memphis on April 29, 2018, to pitch in long relief out of the bullpen. However, he did not make an appearance and was optioned back to Memphis on May 4. He was recalled once again on May 31, and he made his major league debut on June 2, pitching three scoreless innings of relief against the Pittsburgh Pirates at Busch Stadium in a 3-2 walk-off win. He was optioned back to Memphis on July 6. He was recalled on July 24 to make his first major league start that night. In his first MLB start, Gomber threw six no-hit innings vs the Reds before allowing a single to Joey Votto with one out in the seventh inning. He finished the year with St. Louis, compiling a 6-2 record with a 4.44 ERA and a 1.51 WHIP in 29 games.
Pitching style
Gomber throws four pitches: a fastball, changeup, curveball, and a slider. His fastball can reach. In his pre-draft report, Jim Callis commented that his changeup was his best pitch.