Notre Dame claimed a sensational 89-87 win over Rutgers in double overtime in the First Four to book a place in the first round of the NCAA Division I Men's Basketball Tournament.
Notre Dame are 150/1 to win the NCAAB Championship outright, while Gonzaga are rated at 3/1.
In the other First Four games, Texas Southern overcame Texas A & M 76-67, Indiana beat Wyoming 66-58 and Wright State proved too strong for Bryant as they secured a 93-82 victory.
The Fighting Irish will take on Alabama in the first round of the West Regional in San Francisco on Friday after coming through a tough test against the Scarlet Knights.
Notre Dame coach Mike Brey was delighted with his team's victory over Rutgers and he believes that close contest may well go down as the game of this year's tournament.
"If there's a better game in the NCAA Tournament, I gotta see it," he said, via Star Telegram.
"That was an unbelievable college basketball game and they're really good, and tough and fearless. I'm really proud of our group because we just kept hanging in. We've grown a lot in the mental toughness area."
The first-round games take place across Thursday and Friday as the remaining 64 teams battle for a place in the Final Four in New Orleans.
Indiana enter the East Regional and will come up against Saint Mary's in Philadelphia, Wright State take on Arizona in the South Regional in San Antonio and Texas Southern come up against Kansas in Chicago in the Midwest Regional.