The Yorkshireman entered the final round four shots behind Australian Hend but produced a closing 64 to get to 14 under and take the contest to extra holes in the Swiss Alps.
Hend – who lost to Alex Noren in a play-off at this event last season – missed a six-foot putt for victory on the second extra hole but found sand off the tee on the next trip up the 18th and after he flew the green with his second, a par was enough to seal victory for Fitzpatrick.
Fitzpatrick made four birdies and a bogey in his first eight holes to catch up to Hend and when he added further gains on the 10th, 14th, 15th and 16th, the Ryder Cup star held a two-shot lead.
Hend then hit back with a birdie on the 15th and a Fitzpatrick bogey on the 17th set up the dramatic finish.
Fitzpatrick, whose victory saw him become the youngest Englishman to win four times on the European Tour, said: It was absolutely nerve-wracking out there.
“I got off to a great start after the front nine and after the birdie on 10, I just felt like I was out there to compete and trying my best to win. It has been a long day.
“It was a great final round. It was the lowest round of the week for me and it’s probably my lowest round in my competition here. It’s always nice to do it on the Sunday. It’s always very special.
“I supposed no one wants to see Hend losing the play-off again but it’s just one of those things and I felt bad about it. I played really nicely to win today. I love this golf course. It’s fantastic.
“It really suits my game. My parents are here this week. It’s really nice for them to witness my win.
“It’s incredibly great to have them out there with me in tournaments, especially so when it’s a tournament that you win. It’s fantastic.”
England’s Tyrrell Hatton birdied four of his last six holes to finish at 11 under alongside Paraguay’s Fabrizio Zanotti, with another Englishman in Lee Slattery two shots further back.
Scot Duncan Stewart was then at eight under, with former world number one Lee Westwood finishing at level par in his 500th European Tour event.
Defeated rival Hend said he had blown his chance, but praised the way Fitzpatrick held his nerve.
“I had the opportunity and I didn’t take it. It’s just what happens when you don’t take your opportunities.
“I hit a good bunker shot on the 18 in regulation play to get into the play-off.
“I hit that shot when I came back to finish my third round this morning. It was just insane out of the bunker.
“I would love to putt the same way I did in the play-off but it didn’t happen.
“I came back this morning to play the 14th hole of my third round and I made a nice eagle there. It was a good start to the day. I didn’t play as nicely in the afternoon but it is what it is.
“Fitzpatrick played great to win. He’s a good champion.
The United States took a sizeable step towards reclaiming the Walker Cup with a commanding display in yesterday’s foursomes.
Leading 8-4 overnight, the Americans eased themselves to 11-5 and within two and a half points of victory at the Los Angeles Country Club, leaving Great Britain and Ireland in deep trouble ahead of the 10 singles matches.
Norman Xiong and Collin Morikawa led the way with a two-up victory over Connor Syme and Paul McBride, although the match was all-square as the pairs left the 15th green before an American birdie at the 16th and a bogey from their opponents at the last proved decisive.
Life proved significantly more straightforward for Will Zalatoris and Cameron Champ, who needed just 13 holes to secure a 6&5 win over David Boote and Jack Davidson, while Doug Ghim and Maverick McNealy were 3&2 victors against Matthew Jordan and Robert MacIntyre.
Only Jack Singh Brar and Scott Gregory registered for Great Britain and Ireland with a two-up success against Braden Thornberry and Doc Redman.