With an eighth and second from the Finnï¿½s two races today, Scott ensured that nobody can catch him going into Tuesdayï¿½s double points Medal Race, meanwhile Dempsey sailed to the silver medal he effectively sealed during Fridayï¿½s racing.
Scottï¿½s victory means that Britain has now won the Finn menï¿½s heavyweight dinghy class at the last five Olympics ï¿½ Iain Percy (Sydney 2000), Ben Ainslie (Athens 2004, Beijing 2008, London 2012) and Scott (Rio 2016).
And it clearly meant everything to the 29-year-old four-time World Champion.
He said: ï¿½I know what it means to me because I know how it made me feel towards the last stages of that final race. I found myself welling up, in tingles as it slowly dawned on me what I had done and I wouldnï¿½t put myself down as the emotional sort but I had a little cry to myself, which I like to think I donï¿½t do that often.
ï¿½The emotions that end come out of you in that situation you canï¿½t really prepare yourself for, it was amazing. If you had asked me if I would win the Olympic Games with a race to spare I would have said absolutely not because of Rio as a venue.ï¿½
Dempsey, meanwhile, was equally effusive after becoming the most decorated male windsurfer in Olympic history, after todayï¿½s fourth in the RS:X Menï¿½s Medal Race confirmed his place on the podium.
He said: ï¿½Being the most decorated male Olympic windsurfer is awesome, something Iï¿½m incredibly proud of. I have been working for a long time, and itï¿½s very hard to stay at the top for that long. Iï¿½m not sure I can do it again. I would love to if I could.
ï¿½I love the Olympics, I think it is the best thing in the world everything that it stands for, I think, is pretty special.ï¿½
Elsewhere on the water in Rio today, Hannah Mills and Saskia Clark maintained their medal charge with eighth and first place finishes giving them a four-point advantage over Annie Haeger and Briana Provancha (USA) at the top of the pile, with the final three races of their scheduled 10-race opening series set to be contested tomorrow.
Clark said: ï¿½Itï¿½s a big day tomorrow, three races so thatï¿½s another 60 points it is possible to get on the scoreboard. The chasing pack arenï¿½t that far behind and everyone really wants this badly so we have to just keep to what we know, keep doing our processes and go from there.ï¿½
Bryony Shaw admitted she felt ï¿½unfulfilledï¿½ after finishing her Rio 2016 in ninth overall after finishing sixth in the RS:X Womenï¿½s Medal Race and she was left reflecting on what might have been in Rio.
She said: ï¿½I had a good cycle in the build up to 2012 and didn't have a great Games and the same has happened here. It's potentially a worse scenario here as I was in good health and good form, so this time it's come down more to mistakes and misfortune. Hopefully I'll come back stronger for the next one.ï¿½
There was disappointment too for Luke Patience and Chris Grube, who suffered a setback to their medal hopes after a starting disqualification in race one of the day saw them drop to 10th overall. Not that Patience is about to give up the fightï¿½
ï¿½Iï¿½m forever optimisticï¿½, he said. ï¿½What happened to us today can happen to our competitors tomorrow. We come back tomorrow, turn the burners on and hopefully make it good and something that were proud of. Itï¿½s frustrating but all is not lost.ï¿½
Defiant Nacra 17 duo Ben Saxton and Nicola Groves were also left insisting, ï¿½Itï¿½s not over until itï¿½s overï¿½ after two 15th place finishes and a 12th today left them with only an outside shot of a medal in Tuesdayï¿½s double points Medal Race.
They sit in eighth place overall, with 19 points separating them and Thomas Zajac and Tanja Frank (AUT), who currently sit in bronze medal position.
Tomorrow sees Nick Thompson bid to claim Britainï¿½s third sailing medal of the Rio Games as he goes in the Laser Medal Race from 6pm BST while Alison Young also contests the Laser Radial Medal Race at 5pm but is not in a position to secure a podium finish. Both races will take place on the PaÌƒo de AcÌ§ucar (Sugarloaf) course.
To follow the teamï¿½s fortunes at Rio 2016 visit www.rya.org.uk/Rio2016, follow @BritishSailing on Twitter and like us on Facebook at www.facebook.com/britishsailingteam