The Spanish side dropped out of the Champions League after finishing behind Juventus and Manchester United but possessed the cutting edge required to damage Celtic's hopes of progressing in the competition.
Brendan Rodgers' men conceded for the first time in all competitions in 2019 as Denis Cheryshev and Ruben Sobrino netted either side of half-time to put Valencia in complete control of the tie.
And while Celtic huffed and puffed in the closing stages, they were unable to make any inroads on home soil, leaving them needing a huge away victory in the return fixture next week.
1 - Celtic have only kept a clean sheet in one of their last 10 knockout stage games in European competition, failing to win each of the previous eight games they've conceded in before tonight (D1 L7). Ominous.— OptaJoe (@OptaJoe) February 14, 2019
Valencia goalkeeper Neto parried clear Callum McGregor's early low drive, while Scott Bain was extended at the other end to turn away a looping Daniel Wass header.
The two defences largely dominated for the remainder of the first half, but Celtic's run of seven consecutive clean sheets came to an end just before the interval. Sobrino held his run to meet Dani Parejo's pass and then squared for Cheryshev to tap in the opener.
And the roles were reversed within four minutes of the restart as Cheryshev sent over an inviting cross from Valencia's left for the unmarked Sobrino to volley through Bain's legs.
The introductions of Timothy Weah and Odsonne Edouard inspired belated improvement from Celtic in attack, yet Valencia dug in and eased through to full-time without any major concerns.