Agase was born in Chicago, Illinois to an Assyrian father and an Armenian mother. He attended Evanston Township High School, but only played on the school’s varsity football team in his senior year. After graduating, he attended the University of Illinois and played college football there as a right guard in 1941 and 1942. In a 1942 game against the University of Minnesota, Agase scored two touchdowns for the Fighting Illini, becoming only the second guard in college football history to accomplish that feat. The first touchdown came in the second quarter, when Agase stripped the ball from Minnesota’s Bill Daley and ran it back 35 yards. The second was a fourth-quarter fumble recovery in the end zone to give Illinois a 20–13 victory. In another game against Great Lakes Naval Training Station, a military team, Agase had 22 tackles. Under coach Ray Eliot, Illinois finished the season with a 6–4 win-loss record. Agase was named an All-American after the season.  Agase entered the U.S. military in 1943 as America’s involvement in World War II intensified. He was sent to Purdue University for training in the U.S. Marines and played on the school’s football team along with enlistees from other schools. Purdue had won just one Big Ten Conference game the previous year, but the influx of trainees including Agase led to a reversal of fortune in 1943. Coached by Elmer Burnham, the Purdue Boilermakers won all of their games that year and were named Big Ten co-champions. Agase was again named an All-American.

During the following two years, Agase served on active duty in the war. He participated in the battles of Iwo Jima and Okinawa, where he received a Purple Heart after he was wounded in action. He rose to the rank of first lieutenant. Agase returned to Illinois in 1946 and rejoined a Fightining Illini team that posted an 8–2 record and was ranked fifth in the nation in the AP Poll at season’s end. Illinois beat the University of California, Los Angeles in the Rose Bowl Game after the season. Agase was named an All-American for a third time, and received the Chicago Tribune Silver Football as the most valuable player in the Big Ten.

Agase had been selected by the Green Bay Packers in the 1944 NFL Draft, but military service delayed his professional career. Although Green Bay still held the rights to him when he graduated from college, Agase instead signed in 1947 with the Los Angeles Dons of the new All-America Football Conference (AAFC). Agase, however, played just three games for the Dons before he was traded in September 1947 to the Chicago Rockets, another AAFC team. The Rockets finished the season in last place in the AAFC’s western division with a 1–13 record.

The Rockets traded Agase and fellow lineman Chubby Grigg the following year to the Cleveland Browns, who had won the AAFC championship in each of the league’s first two years of play. Led by quarterback Otto Graham, fullback Marion Motley and ends Dante Lavelli and Mac Speedie, Cleveland won the championship again in 1948, posting a perfect 14–0 record and beating the Buffalo Bills in the title game. Another championship followed in 1949, but the AAFC then dissolved and the Browns, along with two other teams, were absorbed by the NFL. Helped by a strong offensive line including Agase, center Frank Gatski and tackles Lou Groza and Lou Rymkus, Cleveland won the NFL championship in 1950. The team reached the NFL championship in 1951 but lost to the Los Angeles Rams. Cleveland lost 24–17 despite gaining more yards and more first downs than the Rams. “It was a very disappointing loss,” Agase later said. “We weren’t quite as sharp as we normally were on offense.”

Before the 1952 season, the Browns traded Agase to the Dallas Texans, a newly formed team set to start play that year. He ended his playing career and signed as a line coach with the Texans under head coach Jim Phelan. The Texans finished with a 1–11 record and folded after the season. Agase came out of retirement briefly after the Texans disbanded, joining the Baltimore Colts and playing as a linebacker for the 1953 season. The Colts finished the season with a 3–9 record, placing fifth in the NFL West division.  Agase was offered a job as an assistant coach for the Colts, but instead joined Iowa State University as its line coach in early 1954 on a $7,000-a-year salary. He and Iowa head coach Vince DiFrancesca had played football together in high school.[28] After two seasons at Iowa, he signed as defensive line coach at Northwestern University. He worked under head coach Ara Parseghian, a former Cleveland teammate.

In seven years under Parseghian at Northwestern, Agase rose to become the coach’s top assistant. When Parseghian was offered the head coaching job at the University of Notre Dame at the end of 1963, he recommended Agase as his replacement. Agase got the job immediately after Parseghian left.  Agase’s first years as coach of the Northwestern Wildcats football team were unsuccessful. The team had losing records each season between 1964 and 1969. In 1970, however, the team finished with a 6–4 record, taking second place in the Big Ten Conference, and Agase was named the national coach of the year by the Football Writers Association of America. The Wildcats followed up with a 7–4 record in 1971, but fell to 2–9 in 1972.

After nine seasons as the Northwestern coach, Agase accepted an offer at the end of 1972 to become head football coach at Purdue, one of the two schools for which he played. Taking the job was “not an easy decision to make,” he said at the time, because he was happy at Northwestern. Agase coached at Purdue through the 1976 season, but his team never posted a winning record in his years there. He was fired in early 1977 and took a job as athletic director at Eastern Michigan University in Ypsilanti, Michigan. He stayed in that job until 1982, when he unexpectedly resigned citing “personal reasons”.

Agase remained active in college football by assisting Bo Schembechler as a volunteer at the University of Michigan until 1987, focusing on special teams. He was named to the Walter Camp Foundation all-century team in 1989 and the University of Illinois all-century team in 1990. Agase was inducted into the College Football Hall of Fame in 1963. He died in 2007 at a hospital near his home in Tarpon Springs, Florida.