Barring a disqualification in Thursday's final, Dempsey is certain to take home at least a silver from his home Championships, held out of the Weymouth and Portland National Sailing Academy, and needs to finish no more than two places behind his Israeli rival to ensure his first ever world crown.
The two title contenders locked horns on the racecourse on Wednesday - Athens bronze medallist Dempsey edged out Mashiah in the first race of the day, finishing second to the Mashiah's third before the Israeli went on the counter-attack in the second race, picking up a second to Dempsey's third.
Dempsey's coach, Barrie Edgington, praised the cool head of his charge on this make-or-break day for the medal hopefuls.
"It was a high pressure day, and Nick sailed a really mature couple of races.
"He just kept on chipping away and made some sensible decisions on the racecourse which have put him right where he needs to be."
Dutchman Dorian Van Rijsselberge - the series leader at the halfway stage of the regatta - proved he's still in with a shot at the podium spots, bouncing back from Tuesday's results of 21, 23, which effectively ended his title hopes, to post 9, 1 on Wednesday and put him back into the bronze medal position.
But there was disappointment for van Rijsselberge's teammate Casper Bouman (NED) who, although not in contention for the podium, dropped out of the top ten medal race positions when he was disqualified from both of Wednesday's races for having been found to have illegally adjusted his mast track.
The Spanish 'dream team' of Marina Alabau and Blanca Manchon are occupying the top two spots of the women's leaderboard.
The European Champion Alabau has dominated the women's fleet since the start of these championships and retains the overall lead heading into the final day of racing on Thursday thanks to 2, 2 from the course today, while Manchon overtakes Poland's Agata Brygola in the silver medal position.
"I have not really been comfortable all day, but I have made up some lost ground at least to be second again," Manchon admitted.
"The goal is to maintain the silver at least, although tomorrow there is predicted more wind so still everything is possible."
France's Charline Picon is poised on the edge of podium spots, just two points off of Brygola in fourth overall, while Skandia Team GBR's Bryony Shaw is out of reach of the silverware in eighth place. She'll hope to end her disappointing week on a high with a strong final race on Thursday to at least equal her previous best RS:X Worlds result of eighth.
Racing at the 2009 RS:X Windsurfing World Championships concludes with the Medal Races on Thursday 10 September.
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.