Valencia's decision to setup on the counter was apparent from the off, as Barcelona took possessional control of the opening exchanges, leaving Lionel Messi to almost produce a moment of magic with a mazing run before being stopped adroitly by Ruben Vezo.
The home side's dominance took the best part of 20 minutes to develop into a meaningful chance, as Messi collected a clever through-ball from Ivan Rakitic, only to fire his effort inches wide of Jaume Domenech's post.
Messi's impact during the opening half grew increasingly more troublesome for the visitors and he soon picked out Andreas Iniesta with a clinical switch of play, leaving Domenech to get a vital touch on the Spaniard's cross as it looked to be making its way to an unmarked Suarez at the back post.
For all of Valencia's attacking deficiencies, the visitors might just have stolen a lead before the break when Martin Montoya broke onto a loose ball on the edge of the box, but the former Barcelona defender saw his volley effort flash wide with Jasper Cillessen looking stranded.
Barcelona started the second period with much the same dominance as the first, although they were almost caught cold when Daniel Parejo sprung a shot from distance leaving Jasper Cillessen to react smartly down low.
Such proved Valencia's stubbornness, Ernesto Valverde decided to introduce new signing Philippe Coutinho just before the hour mark, as the home side went in search of a vital foothold heading into the second leg at the Mestalla.
Coutinho appeared inventive following his introduction, but it was the old faithful that finally hoisted the hosts into the lead, as Messi beat two defenders to pick out Suarez in the middle, who made no mistake with a clinical diving header to make it 1-0.
Barcelona's £145m playmaker might have notched his first goal for the club soon after, only for Domenech to get down low in order to keep out the Brazilian's side-footed effort just over 15 minutes from time.
The hosts' advantage never really looked like being threatened in the final throes of the match, although Valencia arguably did well to ensure that they went back to the south coast just one goal behind with another 90 minutes to be played.
BARCELONA (4-4-2): Cillessen; S. Roberto, Pique, Umtiti, Alba; A. Vidal (Coutinho '58), Iniesta (Alcacer '73), Rakitic (Paulinho '68), Busquets; Suarez, Messi
VALENCIA (4-4-2): Jaume; Montoya, Paulista, Vezo, Gaya; C. Soler (Torres '76), Parejo, Coquelin, Pereira (Maksimovic '46); Rodrigo (Mina '81), Vietto