In an October 1953 game against Duke at the Polo Grounds in New York City, Mischak made an improbable play to seal a 14–13 Army victory that was chronicled in David Maraniss' biography of Vince Lombardi, When Pride Still Mattered. Late in the fourth quarter, Duke running back Red Smith ran a double reverse for what would have been a go-ahead touchdown, but was pursued by Mischak from 73 yards behind. As Smith neared the endzone, Mischak caught up to him and made a touchdown-saving tackle short of the goal line. Two subsequent stops by the Army defense yielded a historic victory for head coach Red Blaik. Col Blaik was later to write “In somehow catching and collaring (Smith), Mischak displayed heart and a pursuit that for one single play I have never seen matched."
In 2017, Mischak was posthumously enshrined into the Army/West Point Sports Hall of Fame, and was named no. 7 on NFL.com's list of Top Ten All Time NFL Players from service academies.