After a promising rookie year, Rozema never won more than nine games in a season. In 1978, he finished with a 9-12 record, 11 complete games and an adjusted ERA+ of 124. In 1979, he again had an above-average adjusted ERA+ of 124, but he started only 16 games and had a record of 4-4. Afterwards, Rozema's ERA fell off to a rate only slightly better than the league average, as he won six games in 1980 and five in 1981.
The 1982 karate kick and reputation as an all-time Tigers character
Rozema got off to a tremendous start in 1982, compiling a 3-0 record and an ERA of 1.63 in his first eight games. In a televised game against the Minnesota Twins on May 14, a bench-clearing brawl erupted after Twins pitchers hit both Chet Lemon and Enos Cabell. Rozema then came running out of the dugout and attempted to deliver a flying karate kick to the Twins' John Castino, but he missed Castino and tore eight ligaments in his knee. As a result, Rozema had to be carried off the field on a stretcher. He required a knee surgery the next day and was put on the disabled list for the rest of the 1982 season. In October 2006, Sports Illustrated selected Rozema as one of the "10 Greatest Characters in Detroit Tigers History". His selection was based on the "karate kick" misfire, a subsequent injury the same year in which Rozema fell on a flask in his back pocket and needed 11 stitches in his hip, an incident in which he shoved a bar glass into the face of teammate Alan Trammell resulting in 47 stitches near Trammell's eye, missing a team bus when he overslept after judging a wet T-shirt contest, and using Brillo pads to wash his new car. On July 9, 2008, the minor league team in Rozema's home town, the West Michigan Whitecaps, gave away an unusual promotional item, "Dave Rozema Karate Kick Bobbleleg" figures.
Later years: 1983-1986
Rozema came back from the injury in 1983 with an 8-3 record and 3.43 ERA in 105 innings pitched. In addition, he played on the 1984 Tigers team that won the World Series. During the regular season, he started 16 games, compiling a 7-6 record with a 3.74 ERA in 101 innings pitched, but did not appear in the post-season. On December 27, 1984, Rozema signed as a free agent with the Texas Rangers a contract for an estimated total of $500,000 to $600,000. He appeared in 34 games for the Rangers in 1985 and had a 4.19 ERA in 88 innings pitched. After compiling a 5.91 ERA at the start of the 1986 season, Rozema was released by the Rangers during the midseason. He then was signed as a free agent by the Chicago White Sox on May 20, 1986, but did not play for them. In a 10-season career, Rozema posted a 60-53 record with a 3.47 ERA in 248 pitching appearances, striking out 448 batters while walking 258 in 1106 innings of work.