In a close encounter with few clear-cut chances, it was a moment of brilliance from the Spain international that opened the scoring, as the Che frontman hit a first-half volley, with Haedo Valdez sealing the win in injury time.
And while the forward spoke of his delight at beating a direct rival in La Liga, he is optimistic that Valencia's performances away from Mestalla will improve following a spirited display against the Rojiblancos.
"I wish we knew what the key to victory is but we have to find the same motivation we have at home in away games," he said after the match. "We can't afford to drop more points.
"We showed great confidence; it was a tough and very important match. My goal was more important than it was beatiful, for sure.
"Today was the day for us; we had to perform against a direct rival who were quite far ahead of us in the table."
Atletico Madrid came unstuck in their attempts to continue their unbeaten start to their league campaign, and Soldado added: "We had some problems scoring in last week's game but we managed to do so this weekend.
"I think we competed at a great level and have beaten a very confident rival, who were on an amazing winning streak."