The 31 year old Warren double-bogeyed the 15th, then bogeyed the next two for a one under par 71.
Singh, who on a dream Sunday at Castle Stuart Golf Links also claims a spot in next week’s Open Championship, came from five shots back and joint 16th place for the fourth victory of his European Tour career.
“I was just enjoying a cup of tea and some chocolate cake and watching it on television, and suddenly got excited,” said Singh - who was three shots behind Warren when he signed his card.
“I think God has been kind, and I think the field came back and I put myself in a to go in for a play-off - I'm very fortunate.
“I would like to thank a lot of people who have been by my side the last three, four years that have been a struggle for me with the injuries: My family, my friend who coaches me, Janet, who was on my bag, my sponsors who stood by me like Callaway, UPS, Societe Generale, golf in DUBAi; all of these guys have been great and supported me through a tough time and I want to thank them all for this.
“It has been really tough - frustrating than anything else. You feel like your game is coming back and another injury creeps up, but I just stuck myself in there and said that you need to work on the physical side, and I worked hard on that. Everything has paid off, and I just want to think about the good things and not what's past and I want to look towards the future now.”
After playing the first 14 holes in a brilliant five under par in the first windy conditions of the tournament it all started to go awry on the 423 yard 15th for Warren.
He faced a 15 foot par putt after finding rough off the tee, but three-putted it for a double bogey six.
His next drive found gorse and after a penalty drop led to a bogey five, then he chipped far too strongly on the short 17th and let another shot go.
Suddenly he needed to birdie the par five last to be in the play-off, but into the wind he needed three to find the green and then missed from 25 feet.
“I might need a little help to get to sleep tonight," said Warren.
"It's going to be disappointing watching The Open (an event the former Omega Mission Hills World Cup winner has never qualified for). I had it in my hands."
Noren was equally gutted minutes earlier as he had taken a bogey six at the last - one behind Singh, who had set the target of 17 under par with a bogey-free 67 - the Swede missing a three foot par putt.
Molinari, who started with a course record 62 and led after the second and third rounds as well, required a closing birdie to win and so emulate his brother Edoardo, winner of the title two years ago.
But he left himself having to hole from nine feet to keep his title hopes alive. He made that, but he could not match Singh's four when they played the hole again.
Singh was assured of The Open spot going into sudden death because Molinari was already exempt for Royal Lytham.
It will be only his second appearance in the event after he missed the cut at Carnoustie five years ago.
"I just love links golf," Singh said, although he had a different opinion when he first experienced it as a 16 year old in 1988.
That was for the qualifying rounds of the British Amateur Championship at Royal Porthcawl and also Pyle and Kenfig. He shot 87 and 84.
"I thought 'My God, this is tough'. I wasn't used to wearing raingear."
Singh's father Milkha was known as "The Flying Sikh", most famous for losing out on an Olympic 400 metres medal in a photo-finish in Rome in 1960.
A Bollywood film is currently being made about his life called "Go Milkha Go", but on the final day in the Highlands it was a case of "Go Jeev Go".
He birdied four of the first six holes, then added another on the 363 yard tenth and parred in.
It looked like three-putting the 337 yard 16th after driving the green and leaving a 14 foot attempt on the last short of the hole would cost him - before those in the final groups started to struggle.
Molinari finished runner-up for the second week running. Victory would have taken him from tenth to second in The Ryder Cup standings, but he is still looking good for a second successive cap.
“It was a good week, positive,” said Molinari. “It’s obviously disappointing at the moment not to finish it off.
“The two putts at 15 and 16 that I missed made all the difference in the end.”
World Number One and defending champion Luke Donald stays sixth on the points table after finishing 16th with, among others, Phil Mickelson and Padraig Harrington.