Poulter, who began the final day with a two-stroke lead, recorded a three-under-par 67 to win by a stroke with a 22-under par total.
Dyson, winner of the tournament in 2000, started his round three shots behind Poulter but went into the lead when he birdied the seventh hole to go five under for the day.
A bogey at the eighth, however, checked his progress and he finished with a 65 to share second place on 21 under par with 17-year-old Italian Matteo Manassero, who signed for a 62.
Poulter, 34, recovered from finding a greenside water hazard at the third hole to record three birdies in his next four holes before effectively sealing a 12th professional title with an eagle at the par-five 13th.
"It feels more than good to win because the last two weeks I've been really disappointed," Poulter told reporters.
"In Shanghai (HSBC Champions) I was lying fourth with six holes to play, and last week (Singapore Open) I was in a position to again win and didn't do it.
"But I've played great all week this week and today I actually played better to shoot three under than I did in shooting 10 under on Friday.
"I don't think I have hit so many good shots...for a long time so it was nice. I felt calm all day. I felt as if I just kept going about my business, I'd make a few birdie putts and that would be enough to win. It's very pleasing to do so.
"It's nice to be back inside the top 10 on the rankings especially after being number five earlier this year in winning the Match-Play Championship," he said.
"The next goal is to get to number eight and then back up to number five."
The 17-year-old Manassero won 157,093 euros to take his earnings to 846,705 since he turned professional in May and said he was looking forward to the season-ending Dubai World Championship, which starts on Thursday.
"It was a fantastic day for me as I started the day quite far behind. Poulter was at 19 under par and I was 13," he said.
"I played some great shots today so I'm very happy with the way I tried to catch the leaders.
"I go to Dubai tonight and it's going to be a great week. I've made the top 60 and it's been a great year and a good way to finish it."
U.S. Open champion Graeme McDowell also heads to Dubai having cut Martin Kaymer's Race to Dubai lead by a further 76,689 euros in finishing fifth on 18 under par.
"It's been another great week and I'm taking some great form to Dubai and that's the key," the Northern Irishman said.
