The Chile international scored twice, and also teed Neymar up for a goal, as the Blaugrana made it eight wins out of eight in la Liga
The Spanish champions were without the injured Lionel Messi, but the Chile international stepped up in his place as he equalised with a wonderful strike after Javi Guerra's surprise opener.
Valladolid caused their hosts problems in the first half, but it was one-way traffic in the second period as Xavi, Sanchez and Neymar completed the rout to extend their 100 per cent start to the league season.
After their battling win over Celtic in the Champions League, Gerardo Martino made only three changes as Alex Song, Alexis and Cristian Tello replaced Sergio Busquets, Pedro and Andres Iniesta.
Valladolid's last match saw them draw 2-2 with Malaga and Juan Ignacio Martinez reintroduced Zakarya Bergdich, Omar Ramos and Fausto Rossi into his starting XI.
The visitors took a surprising 10th-minute lead at Camp Nou as Guerra rose above Adriano to head Patrick Ebert's corner for his fourth league goal of the season, but it did not last long.
Barcelona drew level within four minutes as Alexis marched towards the area and drilled a fearsome strike into the top corner of the goal.
The home fans were incensed around the half-hour mark as Carlos Pena blatantly tripped Neymar inside the area, but referee Jesus Gil made the questionable decision to give the hosts nothing.
Barca were left frustrated as Sanchez screwed a shot wide and Xavi blazed a free-kick over the crossbar to send the sides in level at the break.
Valladolid came out after half-time undoubtedly looking to keep things tight initially, but Barcelona took the lead within seven minutes.
Neymar surged at the Valladolid defence before picking out Tello to his left, and the winger crossed low into the area for Xavi to direct the ball into the bottom far corner.
A few moments later, Tello was involved again as he cut in from the left, but this time he went for goal himself only for his effort to crash off the crossbar.
Barca did add a third in the 64th minute, however. After an excellent through-ball from Neymar, Alexis cruised into the area and confidently fired past Diego Marino.
Six minutes later their roles were reversed. Alexis found himself played into the area, but instead of shooting the Chilean squared to Neymar, who calmly placed a shot into the bottom corner.
The vibrant Neymar went in search of his second of the match as he cut in from the left, but he sent his effort comfortably over Marino's crossbar and Alexis headed straight at the keeper as the hosts were made to settle for their three-goal triumph.