Ivan Rakitic deflected Guilherme Siqueira's cross-shot into his own net to give Valencia a shock lead.
Santi Mina then finished a terrific move by slotting in a second goal in first-half stoppage time.
Messi ended a club goal drought of 515 minutes, but Barcelona now only lead Atletico Madrid on goal difference.
Luis Enrique's side began April with a nine-point lead over second-placed Atletico, but their season has crumbled since then, with defeat against Real Madrid in El Clasico marking the start of a dreadful run.
It was Atletico who ended Barcelona's chances of retaining the Champions League in midweek, and who drew level at the top of La Liga with a comfortable 3-0 victory over Granada earlier on Sunday.
Barca, playing the 53rd match of a draining season that included a trip to Japan in December to win the Club World Cup, looked weary and short of ideas as they attempted to fight back from a 2-0 half-time deficit.
They could lose top spot if they fail to win at Deportivo La Coruna on Wednesday, with Atletico visiting Athletic Bilbao on the same night, and Real Madrid - just a point behind in third place - also in action, at home to Villarreal.
It was Atletico who ended Barcelona's chances of retaining the Champions League in midweek, and who drew level at the top of La Liga with a comfortable 3-0 victory over Granada earlier on Sunday.
Barca, playing the 53rd match of a draining season that included a trip to Japan in December to win the Club World Cup, looked weary and short of ideas as they attempted to fight back from a 2-0 half-time deficit.
They could lose top spot if they fail to win at Deportivo La Coruna on Wednesday, with Atletico visiting Athletic Bilbao on the same night, and Real Madrid - just a point behind in third place - also in action, at home to Villarreal.
