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.