The 31-year-old Que outlasted a battling Rodgers with a par at the first extra hole after both players finished tied on six-under-par 278 in regulation play at the Seri Selangor Golf Club.
Thailand's Thaworn Wiratchant finished third, one shot out of the playoff, after a 68 which included a costly double bogey on his last hole while Australians Scott Hend and Brad Smith shared fourth place with Filipino Juvic Pagunsan on 280.
Taking a one-shot lead into the final round, Que, whose last victory was at the 2008 Philippine Open, carded a 70 in the final round and was caught by playing partner Rodgers, who closed with a 69.
But the Englishman was forced to settle for his fourth runner-up finish in Asia after making mistakes in the play-off to allow Que to snatch victory and the winner's check of $59,717.
"It feels great. First time I won was in 2004 and then I waited for four years for my second win. Now I've just waited for two years for my third. It's good and a great feeling. Hopefully I'll keep winning and I won't stop," said Que.
"Three is a charm. Winning a third time tells you that you can really do it no matter what. You just need to have the right mind set and believe in yourself that you can do it." Rodgers, who was searching for a second victory after his 2006 Pakistan Open victory, took the defeat in his stride.
"Finishing second is never fun. It was neck-and-neck and it was done in good spirit and good fun. We were battling away in a good way as we've known each other for a long time. It is a good tournament for me but a disappointing finish," said Rodgers.
Thaworn, bidding for a record-equalling 12th Asian Tour victory, charged up the leaderboard with five birdies, including four in a row, on his back nine but stumbled badly with several poor shots which included one that landed in the hazard on 18.
"I hit it too much right with the driver and then found it difficult from there on. I've always said that this course was a tough one," said the Thai veteran.
Airil Rizman finished as the leading Malaysian in tied 14th place after closing with a 74 for a 284 total.
Germany's Alex Cejka shrugged off gusting winds to take a one-shot lead after Friday's second round at the Turning Stone Resort Championship in Verona, New York.
The 39-year-old, seeking his maiden PGA Tour title, fired a sparkling four-under-par 68 at Atunyote Golf Club for a 10-under total of 134.
Cejka covered the back nine in four-under 32 to end the day a stroke in front of South African Rory Sabbatini (70) and American Chris Tidland (69).
Australian Steve Elkington carded a 71 to share fourth place at seven-under with Britain's Brian Davis (71) and Americans Robert Garrigus (69), Woody Austin (69), John Mallinger (70) and Omar Uresti (72).
Cejka, a stroke off the pace when the weather-delayed first round was completed earlier in the day, was delighted to claw his way to the top of the leaderboard as winds gusted up to 60kph.
"Today, with the gusts, it was tricky but I hung in there," the Czech Republic-born German told reporters after recording six birdies and two bogeys.
"I shot even par on my front nine and then four under on my back, so I'm very pleased to be in this position." "Two rounds to go and a lot of things can happen but I'm playing well," added Cejka, who has twice finished second on the PGA Tour since joining the circuit in 2003.
"We'll see what happens. If I keep playing like the last two days, I'll be very pleased." The cut fell at two-under 142 with 72 players qualifying for the weekend. Among those missing out were former major winners Todd Hamilton and Shaun Micheel.
Most of the PGA Tour's biggest names are competing this week in the third World Golf Championships event of the year, the WGC-Bridgestone Invitational at Firestone Country Club in Akron, Ohio.
