Hakim Ziyech broke the deadlock in stunning fashion eight minutes in, setting the tone for a thrilling tussle which could have swung in Valencia's favour had Parejo not skied his spot-kick.
Quincy Promes thumped in Ajax's second after Parejo's miss and the woodwork denied both Rodrigo and Ziyech before half-time.
Dusan Tadic – who teed up Ziyech's opener – passed up a golden chance to further Ajax's lead after the interval, but he atoned by setting up Donny van de Beek, who duly ensured last season's semi-finalists made it two wins from two.
Jasper Cillessen had to keep his former club at bay inside the opening 25 seconds, although Van de Beek's effort would have been disallowed for offside anyway.
Cillessen, though, was left flapping at thin air as Ziyech sensationally picked out the top-left corner with a pinpoint strike.
Edson Alvarez's lunge on Goncalo Guedes gifted Valencia a reprieve, only for Parejo to lash the resulting penalty high over the bar after 25 minutes.
Valencia were made to pay nine minutes later – Promes slamming home from Van de Beek's lay off.
Rodrigo looked sure to haul one back but his flick was kept out by a combination of the upright and Andre Onana, before Ziyech clattered another wonderful effort off the bar at the other end.
Onana twice came to Ajax's rescue after the restart, tipping Rodrigo's nudge onto the post moments after getting to Ferran Torres' shot.
Tadic should have compounded Valencia's frustrations soon after but instead side-footed wide from close range, while Promes also thrashed over.
But those misses mattered little when, at the culmination of a slick move, Tadic found Van de Beek, who wrapped up the points with a typically composed finish.
What does it mean? Ajax 2.0 a force to be reckoned with
Frenkie de Jong and Matthijs de Ligt may no longer be in Ajax's ranks, but Ten Hag's side have started their Group H campaign in the style you would expect from a team which conquered Real Madrid and Juventus en route to last season's semi-finals.
Ajax, who have now won five successive away Champions League matches, seem to have grown in stature despite the loss of their two young stars and with the attacking talents they possess, Ten Hag's project has a real sense of longevity about it.
Ziyech makes his mark... again
With all the talent available to Ten Hag, it is easy to forget just how good Ziyech was in Ajax's run to the semis, scoring five goals and proving to be one of the best playmakers in the competition.
Though while De Jong and De Ligt moved on, Ziyech stayed despite reported interest from some of Europe's elite clubs, rather surprisingly signing a contract extension in August. His quality – as evidenced by his sublime opener and the later shot which rattled the woodwork – is in no doubt, though, and it surely cannot be long until the big boys come calling.
Parejo loses his cool
Penalty misses from Parejo do not come along often, but his effort in the first half may be one of the worst attempts Valencia's captain has ever had from 12 yards.
The Spain international has scored three spot-kicks already this term, but – after a slightly longer wait while VAR confirmed the referee's decision – he certainly lost his composure this time around.
Valencia are back at the Mestalla on Saturday, taking on Deportivo Alaves in LaLiga, while their next group game comes against Lille on October 23. ADO Den Haag are Ajax's Eredivisie opponents on Sunday, with a home clash against Chelsea their next continental fixture.