Two-time world rally champion Sainz, father of McLaren Formula 1 driver Carlos Sainz Jr, finished 6m21s clear of reigning champion Nasser Al-Attiyah after 12 stages.
Representing X-raid Mini in this year's event, Sainz will now have won the Dakar with three different manufacturers, having previously triumphed with Volkswagen in 2010 and Peugeot in 2018.
The victory is X-raid Mini's first since its four successive triumphs between 2012 and 2015, and a first for the Mini John Cooper Works Buggy model it had debuted in the 2018 Dakar.
Having bagged four stage wins over the course of the marathon, Sainz and co-driver Lucas Cruz arrived into the final day of competition with a 10-minute buffer over Al-Attiyah and Stephane Peterhansel.
It never came under serious threat as he paced himself through the shortened 167km stage, surrendering only four minutes to Al-Attiyah.
Sainz now only needs to arrive at the finish line in Qiddiya for his victory to be made official.
Though he missed out on victory, Al-Attiyah will have capped off a sixth podium in the last seven editions by beating Peterhansel to the runner-up spot.
With only six seconds in hand over Peterhansel to start the day, Al-Attiyah caught and overtook the Frenchman's road-opening Mini buggy to cement himself in second place.
He also picked up his first stage win of the 2020 Dakar at the very final attempt.
Behind Peterhansel, who will celebrate his 17th Dakar podium, local driver Yazeed Al-Rajhi took his best Dakar finish yet in fourth place in his Overdrive Toyota.
Al-Attiyah's Toyota Gazoo squadmates Giniel de Villiers and Bernhard ten Brinke made it four Hiluxes in the top seven, the pair separated by sixth-place finisher Orlando Terranova in the X-raid Mini 4x4.
The 2020 marathon featured two first-time stage winners in Vaidotas Zala, a newcomer to the Mini ranks, and Mathieu Serradori, who was a standout eighth at the finish in his Century buggy.
Two-time Formula 1 champion Fernando Alonso passed the final stage 3m25s slower than Al-Attiyah, good enough for fourth-fastest on the day - behind also Yasir Seaidan (Mini) and Terranova.
Alonso has completed his maiden Dakar in 13th place overall, trailing Sainz by over four and a half hours at the marathon finish - as a consequence of lengthy repairs on the second stage and a roll during the 10th.
This was the first time since 2015 that no Peugeot finished in the top three, or indeed the top 10, in the Dakar.
Khalid Al Qassimi's privateer entry burned up after a promising start, while the other PH Sport-run Peugeot of Pierre Lachaume crashed out on the penultimate day.
General classification (top 10):
Driver / Co-driver
Giniel de Villiers
Bernhard ten Brinke