The prolific attacker was simply unstoppable in Belarus as he helped his side to a crucial away win.
The Spanish side did not have an easy evening against the Borisov outfit before the break, but Roberto Soldado's converted penalty in the dying seconds of the first half helped the club on its way. Soldado made it two after the interval and the Spain international got his hat trick in the 69th minute following a fine finish.
The away side started the match the better team of the two and came close to opening the scoring after only five minutes of play. Fernando Gago reached Soldado with a superb pass, but his powerful strike was kept out by Andrey Gorbunov.
Soldado again caused the BATE defense all kinds of trouble shortly after when he nutmegged Egor Filipenko before setting up Andres Guardado. However, the Mexican winger's shot was too weak to trouble Gorbunov.
BATE then took over the initiative and created a number of dangerous situations, with Vitali Rodionov in particular threatening.
The striker hesitated just too long after being set up by Aliaksandr Hleb, allowing Ricardo Costa to make a last-ditch clearance, while Valencia goalkeeper Diego Alves only just intercepted a low cross from the left before Rodionov could tap home from close range. Meanwhile, Alves wasn't too impressed with the striker's header after Maksim Bordachev's excellent cross.
It was the away side which eventually broke the deadlock, though, and it was Soldado who added his name to the score sheet. Marko Simic pulled down the attacker inside the BATE area, leaving the referee no other choice but to award a spot kick. Soldado stepped up to take it himself, and easily slotted home.
Rodionov once more threatened only minutes into the second half, but Alves again proved to be in fine form. Valencia then broke free on the counterattack, and Soldado doubled his side's lead with a well-taken volley after a Guardado cross from the left wing.
Both Guardado and Soldado could have made it three immediately after, but the former's attempt was blocked by the goalkeeper, while the latter's shot was cleared off the line.
Soldado would eventually get his third of the evening. Tino Costa managed to reach the prolific attacker despite the duo being outnumbered by the BATE defence, and the 27-year-old again showed his class with a calm finish.
Valencia and BATE have both collected six points from three games, and share top spot with Bayern Munich. Both sides meet again at Mestalla on Nov. 7.
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