The Spanish Citroen driver had entered Sunday's final two stages of the event with a lead of less than one second over the Ford of Neuville, with the Belgian himself chasing his first win in the series.
Sordo, who had previously finished on the podium 34 times without standing on the top step, started strongly on the first run through the Dhrontal stage, taking 2.2 seconds out of Neuville and his Qatar World Rally Team Ford to extend his advantage to three seconds with only the repeat run through the same test to come.
That left Neuville needing to produce a spectacular time on the final stage, but he cracked under the pressure and a trip off the road ensured Sordo took the spoils by a final margin of 53 seconds.
Mikko Hirvonen made it two Citroens on the podium as he took a solid third position, with Martin Prokop a distant fourth.
Robert Kubica was an outstanding fifth as he took the win in the WRC2 class, ahead of Welshman Elfyn Evans.
It is Kubica's third success in four rallies and he now leads the class standings.
Jari-Matti Latvala recovered to seventh place after his chances of winning for Volkswagen were ended by a crash on Saturday.
Hayden Paddon, Mads Ostberg and Evgeny Novikov rounded out the top 10.
Championship leader Sebastien Ogier, who crashed his Volkswagen on Friday, salvaged three points from the event as he set the fastest time on the final 'Power Stage'.
The Frenchman still leads Neuville by 75 points with four rounds remaining.