There was no such tension in the girls' event, where Hayley Davis successfully defended her crown well clear of the pack, finishing six shots clear of Lauren Taylor with a winning score of five-under.
Mullen, from Royal North Devon Golf Club, had led the first two rounds and was one shot clear going into the final hole. But an amazing up-and-down from Hendry sent the tournament into sudden death. Both players finished on three-under.
Mullen, 17, had a great opportunity when they played the 18th for the third time, but he three-putted after making the green in two, and Hendry finally triumphed on the fourth play-off hole.
Hendry, also 17, is from Aberdeen but plays his golf in Dubai. He was given a sponsor's invite to the tournament.
He said his up-and-down on the final regulation hole was the best of his life. He said: "I kept going on the front nine but it was rollercoaster play. We both played great and I think it deserved a play-off like that. It was great experience for the two of us and it felt like we had been out there all day."
A dejected Mullen said: "I should have won. I hit 15 greens but finished two over par. My bunker play was great but I putted too much."
In the girl's event, Davis had a four-shot lead going into the final round but saw the deficit cut to just one early as Taylor, of the Woburn Golf Club, picked up a couple of birdies.
Davis kept finding the bunkers on her front nine but steadied herself on the way home to win comfortably.
She said: "I didn't play great and it was very up and down. I was trying to get a good rhythm and it felt good to come back at one under." The competition was open to youngsters who were under 18 years old at the start of the year.
Most players qualified for the event through junior championship tournaments at their own golf clubs.