Zimmerman was a "triple-threat" player as a runner, passer, and kicker on coach Bernie Bierman's and Tex Cox's Tulane football teams from 1929 to 1932. His first three years saw three Southern Conference championships. Zimmerman led the Green Wave to a win-loss-tie record of 25–4–1. Tulane football legend Jerry Dalrymple started playing the season before.
The 1931 team lost only to national champion USC 21 to 12 in the Rose Bowl in which Zimmerman threw a touchdown to Vernon Haynes. Down 21 to 0 in the third quarter, Zimmerman led a running attack which ended with a 6-yard pass to Haynes for the score. Tulane's other score was a run by Wop Glover set up by 11 and 15 yard passes from Zimmerman to Dalrymple. Tulane still managed a Rose Bowl record for yardage gained. Zimmerman eclipsed 100 yards rushing in both the Auburn and LSU games that year.
1932
The 1932 team saw Zimmerman get then school records with 1,885 yards total offense and a 5.5-yard rushing average. The latter mark still ranks second. Zimmerman was one of three consensus All-Americans from Southern teams in '32, along with Pete Gracey of Vanderbilt and Jimmy Hitchcock of Auburn. Tulane was tied 6 to 6 by Vandy, breaking a Southern Conference winning streak two weeks away from lasting four years. The only score for Tulane came on a 55-yard punt return for a touchdown from Zimmerman. Tulane lost to Auburn, and then lost to LSU in the final game of the year with Zimmerman and several other regulars sidelined by a flu epidemic. "Zimmerman is probably the finest open field runner the South has seen in the past decade" wrote Henry McLemore announcing the United PressAll-America team. He ended his Tulane career as the Green Wave's all-time leader in total offense and pass interceptions, setting records that lasted for 40 years. He also ranks fifth in career rushing yards with 2,369. Zimmerman is a member the Tulane Athletics Hall of Fame and was elected to the Louisiana Sports Hall of Fame in 1975.
Track and field
Zimmerman was Tulane's first Southeastern Conference track champion, winning the 1933 pole vault title. He held the national junior pole vault mark at 13 feet 5 and 7/8 inches, recorded in Lincoln, Nebraskain the summer of 1931.