Raphinha nodded a header over the goalkeeper after a brilliant long pass by midfielder Sergio Busquets who spotted the Brazilian winger ghosting behind the defence into the box in the 15th minute.
Barca could have extended their lead in the 55th minute when Ferran Torres shot a penalty wide of the goal. Five minutes after that, however, they lost defender Ronald Araujo who received a straight red card for a last-man foul on Hugo Duro.
Barca top LaLiga on 62 points, 10 clear of second-placed Real Madrid who will play at Betis later on Sunday. Valencia, who have won only one of their last 10 league matches, are second to last on 23 points.