He played college football for the Wyoming Cowboys and was selected by the Cardinals in the sixth round of the 1985 NFL draft.

Born in Martin, South Dakota, Novacek attended Gothenburg High School in central Nebraska,[1] where he was a two-year starter at quarterback and a three-sport athlete.

[3] Novacek accepted a scholarship from the University of Wyoming in Laramie and started his college football career as a split end.

[4] He had few opportunities to prove his true worth in head coach Al Kincaid's run-oriented wishbone offense, where the team usually threw around 18 passes per game.

After rookie Rob Awalt had a break-out game against the Philadelphia Eagles,[16] Novacek was placed on the injured reserve list on November 2.

The next year with Gary Hogeboom instead of Neil Lomax as the team's starting quarterback, his production fell to 23 receptions for 225 yards and one touchdown.

In 1990, Joe Bugel was hired as the new head coach, who looked for the tight end position to be either a blocker or perform H-back type functions.

He underwent arthroscopic surgery on his right knee to repair a partial tear of his medial meniscus before the last game of the season,[19] but still helped beat the Pittsburgh Steelers in Super Bowl XXX.

In 1996, although he missed the regular season because of a degenerative disc in his back, the Cowboys decided not to put him on injured reserve, in the hope he could be ready for the playoffs.