The Spain striker opened the scoring from the penalty spot just before half-time and struck twice more in the second half to sink surprise package BATE Borisov.
The two teams were joined on six points by Bayern Munich at the midway stage of the group.
BATE had stunningly won their first two games in the group, against Lille and Bayern, but were quickly on the back foot on Tuesday night.
Soldado drew a sharp early save from home keeper Andrey Gorbunov with an angled drive from 12 yards and it set the tone for the early exchanges.
But Fernando Gago's 20-yard effort was not sufficiently well struck to cause problems for the keeper, who then saved comfortably from Andres Guardado.
BATE gradually came into the game and finally threatened Valencia's goal through Dmitry Likhtarovich on the half-hour, but Diego Alves saved with his fists.
Vitaly Rodionov had a header saved and then shot over from long range, before sending a second headed opportunity over the bar.
Alexander Volodko managed to hit the target but his right-footed effort was weak and Alves saved easily.
BATE's spell in the ascendancy came to nothing, though, as they conceded on the stroke of half-time. Marko Simic fouled Soldado in the penalty area and was booked, and the striker took the spot-kick himself and found the bottom corner.
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The lively Rodionov drew another good save from Alves early in the second half but Valencia swept straight up the other end and doubled their lead.
Guardado was the provider, the Mexico international floating the ball into the box for Soldado to volley home from 12 yards.
The Spanish side sought to immediately kill the game off once and for all, with Tino Costa's drive parried by Gorbunov and Egor Filipenko's block delaying Soldado's hat-trick.
Guardado then volleyed Sofiane Feghouli's cross wide and Soldado tried his luck from 20 yards but could not beat Gorbunov, who then blocked another Guardado volley.
But Soldado and Valencia were not to be denied, and he completed his treble in the 69th minute after Tino Costa squared the ball from the right.
He was soon replaced by Jonas Oliveira, although not before watching Ever Banega's lob drift just wide.
Renan Bressan, surprisingly left on the bench by BATE, had been introduced with 15 minutes remaining and the Belarus playmaker shot over as his side sought a consolation goal.
But it was in vain as Valencia followed up their win over Lille.