The 476km stage between Wadi ad-Dawasir and Haradh was a closely-contested affair as four riders were less than a minute apart 300 kilometres in.
Quintanilla was already ahead at that point but he was under pressure from KTM's Price and the Hondas of Joan Barreda and Brabec.
But it was the very last section of the stage where Quintanilla was able to pull away and he won the stage by 1m54s as Price secured second.
Barreda, despite a small crash during the day, was able to take third.
Brabec was only fourth but he still has a 20m53s lead over Quintanilla in the overall standings, with Price and Barreda moving up to third and fourth respectively, both of them demoting Jose Ignacio Cornejo (Honda).
Ross Branch (KTM) was best of the rest in the stage followed by the Benavides brothers, with Kevin (Honda) narrowly outpacing Luciano (KTM) for sixth.
Matthias Walkner lost two and a half minutes right at the start of the stage, and while the KTM rider stayed on pace for much of the stage after that, he dropped to eight minutes behind just before the finish.
KTM's 2018 champion is now 37 minutes away from the leader with three stages to go.
Casale wins quads by three seconds
Ignacio Casale narrowly took the victory in Stage 9 as Alexandre Giroud gave up a 2m25s advantage he had at the last checkpoint.
Casale took his fourth stage win of the event and his overall lead is now up to 44m57s.
The Chilean rider was not fastest at any of the day's six checkpoints and was outside of the top three for most of the day, yet he crossed the finish line in first place.
He was just three seconds faster than Giovanni Enrico as the duo beat Giroud to first and second.
Casale's closest title rival Simon Vitse was eight minutes off the pace.
Standings after Stage 9 (Bikes, top 10):
Jose Ignacio Cornejo