Ross Branch, who took a shock stage win on Monday and consequently was first on the road this time around, damaged his shoulder in a crash and lost over an hour.
Yamaha rider van Beveren was another notable crasher as the Frenchman suffered a heavy fall just three kilometres into the stage and was resigned to his third straight retirement from Dakar.
Van Beveren was diagnosed with a fractured collarbone and a bruised hip and he was taken to the King Khalid hospital in Tabuk.
Paulo Goncalves, who left Honda to lead Indian brand Hero's efforts, meanwhile suffered an engine problem and remains in the stage.
Brabec, meanwhile, controlled proceedings during the 427km stage, crossing all six checkpoints as the fastest rider.
He ended the day with a sizeable 9m39s gap over fellow Honda rider Jose Ignacio Cornejo, and now leads Cornejo in the general classification by 15 minutes.
Cornejo was the only rider to finish within 10 minutes of Brabec on the day, with Joan Barreda (Honda) taking third and Luciano Benavides narrowly beating his brother Kevin to lead KTM's efforts in fourth.
Kevin Benavides, however, holds fourth in the overall standings, completing a Honda 1-2-3-4.
Matthias Walkner (KTM) lost more than 20 minutes, as did Husqvarna's Pablo Quintanilla and Toby Price (KTM), the latter getting lost at the end of the stage.
Price still beat fellow KTM rider Sam Sunderland, who was 38m49s off the pace after entering the day as the marathon leader, and Xavier de Soultrait (Yamaha), who had gone off-route alongside Price.
Enrico beats Casale in quads
Giovanni Enrico denied Ignacio Casale's third straight stage win, but the latter still managed to extend his overall lead.
Casale was fastest at the first four checkpoints, 200kms into the stage, but then was surpassed by Enrico, as well as Simon Vitse.
Enrico beat Vitse by a minute, with Casale a further 35 seconds adrift.
However Casale's main rival in the overall standings is still Rafal Sonik, who lost about 10 minutes in the last part of the stage, and the Polish veteran is now 19m56s behind Casale, with Enrico in a close third.