Kurt Warner (St. Louis Rams) holds the record for passing yards in a Super Bowl with 414 yards against Tennessee in Super Bowl XXXIV. He is also second on the list with 365 yards against New England in Super Bowl XXXVI. Donovan McNabb (Philadelphia Eagles) and Joe Montana (San Francisco 49ers) are tied for third* with with 357.
http://www.nfl.com/superbowl/records/superbowls/player/passing
* UPDATE : Your answer is partially correct. Warner does in fact hold the 1st and 2nd highest yardage in Super Bowl history (414 vs the Titans and 377 vs the Steelers)
But the person that holds the 3rd highest yardage game in Super Bowl history is...you guessed it...Kurt Warner (365 vs Patriots)
The quarterback who holds the record for the most passing yards in a single playoff game is Norm Van Brocklin, with 554 yards.
The quarterback who holds the record for the fewest passing yards in a single NFL game is Jack Concannon, who only threw for -7 yards in a game in 1972.
Todd Ellis
Wuerrfel
Former Bears quarterback Sid Luckman holds this record passing for 7 touchdowns on November 14th 1943.
Kurt Warner
Chuck Hartlieb - 558 yards
Jim Kelly
Kurt Warner
John Stocco
Through the 2010 season, Daunte Culpepper with 4,717 passing yards in 2004.
John Stocco