Rahm closed with a four-under 68 to finish at 13 under at JCB Golf & Country Club on Sunday, claiming his first win on the Saudi-funded circuit.
Australia's defending champion Cameron Smith overcame three early bogeys to shoot a 69 and tie for second with Joaquin Niemann (65) and Hatton (69) on 12 under.
Rahm had three-putted the 17th to drop back into a tie for the lead with Hatton on 13 under par, only for the Englishman to then three-putt the 18th from long range.
Rahm had finished in the top 10 in all nine LIV tournaments he had completed since joining the breakaway league, but was forced to withdraw from the Houston event with a toe injury which also saw him miss the US Open.
The 29-year-old Spaniard, who finished joint seventh in the Open at Royal Troon, alluded to off-course family issues in a post-round interview broadcast by LIV Golf.
"It's just emotional, you know,' Rahm said."It hasn't been the easiest year for our family. Kelly [his wife] and I have gone through quite a bit and she has gone through even more, being on bed rest and many other things.
"She did tell me our son Kepa said to bring a trophy home on this stretch of golf and I started to believe it was going to happen at one point today - maybe not in the last 20 minutes but at least I can bring one home for them.
"To get over the hump feels quite incredible and it's just relief that it happened."
Overnight leader Andy Ogletree looked to be cruising to victory when he birdied the first and second to lead by four and recovered from a double bogey on the eighth with birdies on the 12th and 13th to get back into a tie for the lead.
However, Ogletree then ran up double bogeys on the next two holes to ruin his chances of victory and had to settle for a tie for sixth.
Lucas Herbert did best of Smith's Australian teammates, tied for 20th at five under with Matt Jones a shot further back.
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