The USA-French pairing of Ramey and Martin had started the day of foursomes (alternate shot) seven strokes off the lead but a brilliant nine-under par round of 63 saw them fly to the top of the leaderboard.
That left the final groups under some pressure to reach the target of 25-under and only McIlroy and Lowry, who played together on the Irish Olympic team and for Europe in the Ryder Cup, were able to get there.
After Lowry, the 2019 British Open champion, missed a par putt on the 17th, the Irish pair knew they needed to make birdie on the 18th to get into a playoff by tying the clubhouse leaders.
World number two McIlroy blasted his drive down the fairway and after Lowry's approach shot left him some work to do, the Northern Irishman produced a wonderful chip that left Lowry with a straightforward five footer for birdie.
Ramey and Trainer had been off the course for three hours and it perhaps showed on the first playoff hole, the 18th.
French-born Trainer drove to just behind a fairway bunker but teammate Ramey's 3-wood was hooked far left and after Trainer's chip was short, Ramey missed his putt from off the green, meaning par was the best they could get.
Lowry's approach shot had ended up in a greenside bunker but McIlroy got it safely on to the green and left Lowry with a chance at birdie and victory.
Lowry has conceded that he has been struggling on the greens of late and he missed the seven-foot putt, leaving Trainer with a putt to extend the playoff.
But Trainer missed to hand victory to the Irish pairing.
McIlroy, playing in the event for the first time, was delighted with the win.
"Absolutely amazing. We've had an awesome week here in New Orleans. The crowds all week have been absolutely amazing. To get the support that we've had out there and to have so much fun while doing it, it has been an awesome week, and obviously I feel like it's just a bonus to win at the end," he said.
"But couldn't be better to have this man alongside me to get a PGA Tour win together."
Big points boost
The win was McIlroy's 25th on the PGA Tour while for Lowry it was his third and his first at a PGA Tour sanctioned event since his British Open triumph at Portrush.
Lowry's last win on the DP World Tour came at Wentworth in September 2022 and he said the boost to his position in the FedEx Cup standings were most welcome.
"We felt like coming into the week that we both could do with a big jump in the FedEx Cup, and we both said at the start of the week, let's go and get 400 points each. That's what we've done," he said.
"I nearly feel a little bit bad taking them because Rory carried me a lot of the way. But yeah, they're mine, and they're not going away," he joked.
American pair Ryan Brehm and Mark Hubbard finished third after their even-par round of 72 left them a shot shy of the leaders, after they were unable to get a birdie on the final four holes.
Overnight leaders Zac Blair and Patrick Fishburn of the United States finished tied fourth after a double bogey on the 17th cost them a place in the playoff.
