Hardy, who knocked out defending champion Kevin Marsh in the third round, birdied the second extra hole in the third round to stop Carrigan.
That sets up a quarterfinal meeting with Alan Bratton, who moved on thanks to a 4 & 3 victory over Michael McCoy.
Dave Womack won the third round's first match when he destroyed Jeff Wilson, 6 & 5. Wilson beat Trip Kuehne in the second round, but could not match Womack, who won the second hole and never looked back.
Womack will face Rick Dewitt on Wednesday as Dewitt took out Michael Harrington, 1-up when Dewitt birdied the par-5 18th hole.
Ryan Hybl, who bested Nathan Smith, 1-up in the third round won the 16th hole with a birdie, then held on to eliminate Smith. Hybl drew Tim Jackson, who moved into the quarterfinals with a 3 & 2 win over Marc Peterson.
Carlton Forrester won 3 & 2 over Bill Williamson and will face Gene Elliott Wednesday morning. Elliott also advanced with a 3 & 2 win against Gregory Hunt.
Wednesday will feature both the quarterfinals and semifinals, then it will be a 36-hole final on Thursday.