Elliott Bennett had opened the scoring for Brighton in the third minute of the first-round tie at Adams Park, but the hosts levelled when Adam Virgo was adjudged to have pushed Matt Harrold and the Chairboys striker fired home the penalty.
Brighton's Gavin Hoyte was dismissed for violent conduct just after the half hour, and Wycombe made the extra man tell when Scott Davies rifled home Kevin Betsy's cross.
The hosts were then reduced to 10 men themselves in first-half stoppage-time when Craig Woodman was dismissed for a professional foul on Murray and Nicky Forster made no mistake from the spot to notch his 10th goal of the season.
Murray put Brighton in front again six minutes after the break, only for Jon-Paul Pittman to level once more.
And it was 4-3 to the hosts after 70 minutes when Betsy again crossed for Harrold to score, only for Murray to have the final say for Brighton nine minutes from time.