Originally signed by the Philadelphia Phillies as an amateur free agent in 1949, Face was twice drafted by Branch Rickey, first for the Brooklyn Dodgers before the 1951 season, and again in 1952 for Pittsburgh. He made his debut in April 1953, and began to excel in 1956 when he set a modern Pirates record for games pitched (68), leading the league and breaking the club mark of 59 set by Bill Werle in 1951. In 1957 he saved 10 games for the first time, finishing fifth in the NL. In 1958 the team finished in second place, the first time in his his five years they had placed better than seventh. Face led the NL with 20 saves, and posted his best earned run average to date with a 2.89 mark. He achieved his success almost exclusively with the forkball, which he had learned from Yankees reliever Joe Page. He used the pitch to confound opposing hitters, saying, "It would come in hard and break anyway it wanted to, sometimes in, sometimes out, mostly down."

His most spectacular season came in 1959, when he posted his remarkable 18-1 record, including 17 victories in a row to begin the year after ending 1958 with 5 in a row; he did not surrender a run in the entire month from June 11 to July 12, finishing the year with an ERA of 2.70. Some of his victories came about when first baseman Dick Stuart committed an error to allow the tying run to score, then hit a home run to save the day; Face finished eighth in the MVP voting, and his 18 relief wins also remain the major league record, topping Jim Konstanty's previous mark of 16 set in 1950. Face's .947 winning percentage exceeded the previous record .938 (15-1), set by Johnny Allen in 1937. In 1960 he had his second 20-save season, placing second in the league with 24, which equalled the previous NL record as Lindy McDaniel set a new mark with 26. With the Pirates winning their first pennant since 1927, he also led the league in games again, tying his own team record of 68; the mark would be broken when teammate Pete Mikkelsen appeared in 71 games in 1966.

In the 1960 World Series against the New York Yankees, Face became the first pitcher to save three games in a single Series, since matched by only Kent Tekulve (1979), John Wetteland (4 in 1996), Mariano Rivera (1998), and Troy Percival (2002). Face entered Game 1 with runners on first and second and none out in the eighth inning, leading 6-2; he retired the side, striking out Mickey Mantle and Bill Skowron and getting Yogi Berra to fly out, before giving up a 2-run Elston Howard home run in the 9th but getting a game-ending double play for a 6-4 win. He came into Game 4 with two men on and one out in the seventh inning, leading 3-2, and retired all eight men he faced. In Game 5 he was again brought in with two men on and one out in the seventh, this time leading 4-2, and retired eight of the last nine batters, allowing only a walk to Mantle. The final Game 7 was rougher going for Face, however; he was brought in with two on and none out in the sixth inning, with a 4-1 lead which he surrendered via an RBI single by Mantle and a 3-run home run by Berra. But he settled down, retiring seven of the next eight batters before allowing another 2-run rally with two out in the eighth for a 7-4 Yankee lead. The Pirates came back to score five runs in the bottom of the inning after Face was pulled for a pinch-hitter, and won the game and the Series in the bottom of the ninth on Bill Mazeroski's legendary home run.

Selected an All-Star each year from 1959-61, Face again led the NL with 17 saves in 1961. In 1962 he broke McDaniel's NL record with a career-high 28 saves (one short of Luis Arroyo's major league mark set the previous year), also posting a 1.88 ERA; Ted Abernathy would set a new record in 1965 with 31 saves. Face now had three 20-save seasons at a time when no other pitcher had more than one. Also in 1962, Face passed Clem Labine to take over the NL record with 95 career saves, and then broke Johnny Murphy's major league mark of 107. In 1963 he earned 16 saves; he then suffered two difficult seasons, picking up only 4 saves in 1964 with an ERA over 5.00, and earning no saves in 1965. In 1964, Hoyt Wilhelm took over the major league career saves record. But Face resiliently returned to save 18 games in 1966 and 17 in 1967, finishing second in the NL both years. In 1967 he passed Warren Spahn's mark of 750 to become the NL's all-time leader in games pitched; his record would stand until Tekulve moved ahead of him in 1986.

After 43 appearances and 13 saves in 1968, Face's contract was sold to the Detroit Tigers on August 31, but he made only two scoreless appearances for Detroit. He signed as a free agent with the Montreal Expos in 1969, earning 5 saves in 44 games before ending his career. In a 16-season career, he posted a 104-95 record with a 3.48 ERA and 877 strikeouts in 1375 innings pitched and 848 games. His NL record of 193 saves was not broken until 1982, when Bruce Sutter passed him; Dave Giusti broke his Pirates single-season mark with 30 in 1971. His 802 games with the Pirates equal Walter Johnson's total with the Washington Senators for the most by any pitcher with a single club (some sources list Johnson with 801). Face saved 16 or more games seven times in an era when starting pitchers were more apt to remain in a game they were leading, and seven times had an ERA under 3.00 with at least 40 appearances.