The women's Medal Race was the first to get underway in ideal conditions at the Weymouth and Portland National Sailing Academy on Thursday, with Alabau enjoying a 12 point buffer over her teammate Blanca Manchon (ESP) in silver heading into the final showdown.
Alabau remained in control, just as she has throughout the regatta, with a sixth place in the medal race more than enough to hand her gold, while Manchon finished fourth in the final 10-board race to make it a Spanish one-two in the women's fleet.
"I'm super, super happy," Alabau said.
"It was not such an easy week - I had to focus hard on the beginning of the week as I knew it would be more windy then which I had trained for so I had to do well early on.
"In the end I had a few points for the medal race, so I could have a really relaxed medal race and it was good. I'm very happy to have the gold, and silver too for Spain so my coach is very happy!"
Charline Picon (FRA) completed the podium spots with a bronze for France, while Bryony Shaw (GBR) ended a disappointing world title challenge on a high, clinching the Medal Race win to boost her overall standing to sixth - a best ever World Championship finish for the Skandia Team GBR sailor.
Dempsey, the 2004 Athens bronze medallist, led the men's fleet heading into their Medal Race on Thursday, needing only to finish two places ahead of Israel's Nimrod Mashiah to claim his first ever World Championship crown.
In the end, the Skandia Team GBR sailor forced his opponent onto the back foot and into a rule infringement at the start, and while Mashiah was taking penalty turns, Dempsey got a flying start.
He led the Medal Race from start to finish to seal victory in emphatic style, watched by a large contingent of family and friends, including his double Olympic gold medal-winning wife Sarah [nee Sarah Ayton], out in Portland Harbour.
"It's just awesome," said an elated Dempsey.
"I was a broken man after Beijing - to go into the medal race there joint first and then to come fourth was just heartbreaking.
"This year is what it was all about for me - my whole focus has been on this week. I've always wanted to be world champion so this is probably the pinnacle of my career, and I'm certainly sailing better than I ever have.
"It's funny because although we live here and train here, we rarely actually race here so you never really know how good you are so to win here at the 2012 venue at such a big event is just amazing."
A seventh place in the Medal Race was enough for Mashiah to keep hold of the silver medal position with The Netherlands' Dorian Van Rijsselberge claiming bronze.
Thursday's Medal Races draw to a close a successful RYA-run, UK Sport-supported RS:X World Championships.
"I'm really pleased with how the event has gone," said RYA Event Director David Campbell-James.
"The RS:X class has been a joy to work with and have been really forward thinking in terms of the media and presentational aspects at the event. The race teams on the water have done a really great job as well, so all credit to them and the numerous staff and volunteers who've made the event a success."
Results - click here
Click here for our RS:X World Championships page containing all the news, photos, links to live results and more from this year's RS:X Worlds.
The RS:X World Windsurfing Championships is the second of three back-to-back World Class events being run by the RYA, supported by UK Sport, and hosted at WPNSA. The IWA Junior, Youth and Masters Windsurfing Worlds was held from 22-29 August, with the Skandia Sail for Gold Regatta - the final round of the 2009 ISAF Sailing World Cup series - set to welcome the cream of the World's Olympic Classes sailors from 14-19 September.