Soldado had big shoes to fill at Valencia after Villa left for Barcelona in the close season but he has quickly made his mark after his move from Getafe.
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The striker, who also netted against Bursaspor earlier in the group stage, scored at a corner after 33 minutes and then raced away to seal the win in the 71st. Tino Costa added a third at the end.
Valencia moved up to second in the group behind Manchester United with seven points from four games, going two ahead of third-placed Rangers with two left to play.
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"It was a vital game. We knew it was important we won this one to put our future back in our own hands," Soldado told Spanish television.
"It was difficult because of their style of play and we knew it would be tough to score a goal. The first came after a bit of a rebound at a corner. That allowed us to play our own game, and encouraged them to come out a bit because they had to win."
A high-tempo start saw both sides go close to breaking the deadlock with Juan Mata being denied for the hosts after only four minutes.
Scotland midfielder Naismith streaked away from the halfway line on a counter-attack soon after, and cutting in off the left flank let fly with a fierce drive which came back off the far post in the eighth.
Allan McGregor saved from Mata, who should have done better in the 12th minute, but the game settled down with Rangers camped in their own half until Soldado scored.
McGregor was unable to get to a corner under the bar and Soldado pounced on the loose ball, squeezing a shot inside the near post.
Valencia continued to dominate and McGregor went full length to keep out an Aritz Aduriz header early in the second period, but he was unable to stop Soldado's effort after a swift one-two with Mata on a break.
Rangers struggled to chase the game, though Naismith found himself in space only to head against the post near the end, and substitute Costa volleyed in off the post in the final minute condemning the Scots to their first defeat this season.
"Our objective now is to be first in the group, to beat Bursaspor at home and then get a win in Manchester," Valencia coach Unai Emery told Spanish television.
