Ziyech's stunning strike gave Ajax an eighth-minute lead, before Daniel Parejo missed a penalty for the hosts and Quincy Promes made it two.
An excellent team goal, finished off by Donny van de Beek, capped another eye-catching display by Ajax as they continued to make light of losing Frenkie de Jong and Matthijs de Ligt to Barcelona and Juventus in the close season respectively.
Erik ten Hag's men now lead the group by three points from Valencia and Chelsea after the Londoners edged out Lille 2-1 in France in Wednesday's other game.
Ajax beat Lille 3-0 in Amsterdam a fortnight ago and have now stretched their unbeaten away run in the Champions League, including qualifiers, to 13 matches.
The Dutch champions, who won at Real Madrid, Juventus and Tottenham in last season's competition, wasted little time in forging ahead as Ziyech collected the ball on the right wing, before cutting inside and unleashing a venomous hit that flew into the top corner from 25 yards out.
Albert Celades, who took over as Valencia coach after the controversial sacking of Marcelino, saw his team blow a chance to level as Parejo blazed a horrible penalty over.
The Dutch side made the Valencia captain pay just nine minutes later, as Van de Beek teed up Promes to score after good work by Dusan Tadic.
Moroccan international Ziyech almost repeated his earlier wonder-strike as he jinked inside again and rattled the crossbar, before Rodrigo poked the ball against the foot of the post from close range at the other end.
Valencia kept plugging away in search of a way back into the match, going close through Ferran Torres, but saw their hopes of a comeback ended by another wonderful Ajax goal midway through the second half.
Quick passing opened up the home defence and Tadic slipped the ball through for midfielder Van de Beek, who had plenty of time to settle himself and slot it into the net.