According to Elias Sports Bureau, Bradford became the first rookie in NFL history to pass for at least 300 yards and three touchdowns with no interceptions during a road victory. John Elway was the last rookie to hit 300 yards with three touchdowns and no picks in a game, regardless of location or results (against Baltimore in 1983).
Bradford also became the 11th quarterback over the past five seasons to pass for at least 300 yards and three touchdowns with no interceptions during a road victory.
Check out the list from Pro Football Reference and you'll see that Bradford was the youngest to accomplish the feat during that span (since the 2006 season). Brady has done it five times during the period in question, one more than Brees. Rodgers and Manning have done it three times. Favre has done it twice.
According to ESPN Stats & Information, Bradford joins Kurt Warner and Jim Everett as the only players in Rams history to accomplish the feat.
Bradford's first 300-yard passing game also marks the first in NFL history by a rookie from Oklahoma. The highest before Bradford, according to Elias Sports Bureau: 144 yards, by Hugh McCullough of the Pittsburgh Pirates against the Brooklyn Dodgers in 1939.