In the late 1970s and early 1980s, Gossage was one of the earliest manifestations of the modern closer, with a bold mustache and a gruff demeanor to go along with his overpowering 100 mph fastball.

[2] Respected for his impact in crucial games, Gossage recorded the final out to clinch a division, league, or World Series title seven times.

After the 1976 season, the White Sox traded Gossage and Terry Forster to the Pittsburgh Pirates for Silvio Martinez and Richie Zisk.

He was also on the mound five days later when the Yankees clinched the pennant in the ALCS against the Kansas City Royals, entering Game 4 in the ninth inning with a 2–1 lead and a runner on second base; he earned the save by striking out Clint Hurdle and retiring Darrell Porter and Pete LaCock on fly balls.

He was on the mound ten days later when they captured the World Series title against the Los Angeles Dodgers for their second consecutive championship, coming on with no one out in the eighth inning of Game 6; he retired Ron Cey on a popup to catcher Thurman Munson to clinch the win.

On April 19, 1979, following a Yankee loss to the Baltimore Orioles, Reggie Jackson started kidding Cliff Johnson about his inability to hit Gossage.

Gossage tore ligaments in his right thumb and missed three months of the season which cost the Yankees a chance to win their third consecutive World Series title.

In the first game of a doubleheader on October 4, 1980, Gossage pitched the last two innings of a 5–2 win over the Detroit Tigers, earning his career-high 33rd save as New York clinched another division title.

Gossage recorded saves in all three Yankee victories in the 1981 AL Division Series against the Milwaukee Brewers, not allowing a run in 6+2⁄3 innings, and he was again the final pitcher when they clinched the 1981 pennant against the Oakland Athletics.

In 1983, his last season with the Yankees, Gossage broke Sparky Lyle's club record of 141 career saves; Dave Righetti passed his final total of 150 in 1988.

In 1984, Gossage clinched another title, earning the save in Game 5 of the NL Championship Series and sending the Padres to their first World Series; after San Diego had scored four runs in the seventh inning to take a 6–3 lead against the Chicago Cubs, Gossage pitched the final two innings, getting Jody Davis to hit into a force play for the final out.

During Game 5 of the 1984 World Series versus the Detroit Tigers, after receiving signs from the coaches on the Padres bench and a mound visit by manager Dick Williams, Gossage refused to intentionally walk right fielder Kirk Gibson with two runners on and first base open.

On the second pitch, Gossage and the Padres would regret that decision as Gibson homered to deep right field, clinching a World Series win for the Tigers.

[11] On August 6, 1988, while with the Cubs, Gossage became the second pitcher to record 300 career saves in a 7–4 victory over the Philadelphia Phillies, coming into the game with two out in the ninth and two men on base and retiring Phil Bradley on a popup to second baseman Ryne Sandberg.

Gossage entered a game against the California Angels with two out in the seventh inning and runners on second and third base, trailing 2–1; he picked up the win when the Mariners scored three times in the eighth for a 4–2 victory.

In his final major league appearance on August 8, he earned a save of three innings—his first in over 15 months—in the Mariners' 14–4 win over the Rangers, retiring all nine batters he faced; José Canseco flied out to left field to end the game.

Multiple-inning outings provide more chances for a reliever to blow a save, as he needs not only to get out of the initial situation but also to pitch additional innings in which to possibly lose the lead.

His son, Todd, is a professional baseball player who has played for the Sussex Skyhawks, Newark Bears, and Rockland Boulders of the Can-Am League.

Gossage coached the American League team in the Taco Bell All-Star Legends & Celebrity Softball Game in Anaheim, California on July 12, 2010.

After the ceremonies, the two of them sat together for an ESPN interview on the podium, taking audience questions and gently ribbing each other, especially about the upper-deck home run Kirk Gibson hit off Gossage in Game 5 of the 1984 World Series.