World number 30 Rai led by one shot overnight, but a rollercoaster final day began with Fleetwood moving out in front after opening with a birdie and hitting an eagle at the par-five second.
Four successive birdies on the front nine moved Rai ahead again, only for a bogey at the eighth to hand the initiative back to Fleetwood.
A host of players began to bunch up behind the leaders, including McIlroy. The Northern Irishman eagled the par-five second but it was a run of five successive birdies at the turn that lifted him back into contention, with a birdie at the last moving him to 24 under and the clubhouse lead.
Meanwhile, birdies at the 16th and 17th drew Rai back level with Fleetwood, who saved par with another clutch putt at the second-last to ensure it stayed that way heading to the 18th.
Rai spurned his first chance on the 18th green, but made no mistake on the same hole in the play-off to secure his third DP World Tour Title.
It was his first win on the tour since the 2020 Scottish Open, when he also beat Fleetwood in a play-off.
The Abu Dhabi Championship is the first of two DP World Tour end-of-season play-off events, with the top 70 players competing this week and the leading 50 advancing to next week’s finale in Dubai.
Rai began the tournament 55th in the standings, but this victory means he will go into next week’s event ranked ninth.
McIlroy, who is two behind Colin Montgomerie’s record of eight years as the tour’s number one, leads the Race to Dubai standings by 767 points from Marco Penge, the Englishman who has won three times on tour this year.
Penge carded a final-round nine-under 63 to finish tied for ninth on 20 under alongside Scotland’s Robert MacIntyre and Angel Ayora of Spain.
