Van Buren played college football for Louisiana State University, where he led the NCAA in scoring in his senior season for the LSU Tigers. After leading LSU to victory in the Orange Bowl, he was drafted by the Eagles with the fifth overall pick in the 1944 NFL Draft. Van Buren acquired many nicknames over his career in reference to his running style, including "Wham Bam", "Moving Van", and "Supersonic Steve". He was the driving force for the Eagles in the team's back-to-back NFL championships in 1948 and 1949; he scored the only touchdown of the 1948 NFL Championship Game against the Chicago Cardinals, and in the next year's championship game against the Los Angeles Rams he set postseason records with 31 carries and 196 rushing yards.