The Spanish striker's hat-trick at a festive Mestalla helped Valencia to their biggest victory in Europe's elite club competition, one goal short of Liverpool's record 8-0 destruction of Besiktas in 2007.
A scoring draw for Unai Emery's side in their final game at Chelsea on December 6 would be enough to secure a berth in the knockout round after the English side were upset 2-1 in Germany by Bayer Leverkusen, who sealed their place in the last 16.
"We achieved our objective and our players will grow in confidence because of that," Emery said at a news conference.
"We need to remain focused now and to forget about tonight's game even though it was a beautiful one for us and one in which we managed to score a lot of goals."
Valencia started at a high tempo despite the rain-sodden pitch and forward Jonas breached the Belgian defences when he headed home in the 10th minute.
The Brazilian sent Soldado clear to make it 2-0 three minutes later with a low shot past Genk goalkeeper Laszlo Koteles and the pair combined again in the 36th minute when Soldado raced away from his markers and struck a powerful shot high into the net.
He completed his hat-trick in the 39th with a tap-in at the far post from a Pablo Hernandez centre, his fifth Champions League goal of the campaign.
COMPLETE GAME
Pablo, who took the captain's armband when Soldado was replaced by Aritz Aduriz, curled in a fifth in the 68th minute, Aduriz muscled his way through the defence to make it 6-0 two minutes later and Tino Costa added the seventh in the 81st.
Victory took Valencia up to eight points from five matches, level with Chelsea and one behind Leverkusen. Genk have two points and have no chance of qualifying or securing the berth in the Europa League for the team that finishes third.
"We played a complete game and now we are left with our last chance against Chelsea in our final encounter which if we win will qualify us," Emery said.
"We started tonight with a high level of intensity and we tried to score as many goals as we could as we knew that could be important in terms of the group standings."
Soldado's performance, coming after his double against former club Real Madrid in La Liga at the weekend, will boost his chances of a recall to the Spain squad for next year's European Championship in Ukraine and Poland.
The 26-year-old, who was born in Valencia and was given a rousing ovation by the home fans when he was substituted, has represented the world and European champions only twice, back in June 2007, when he failed to score.
Pressure has been mounting on Spain coach Vicente del Bosque to pick Soldado, one of the nation's best forwards along with Barcelona's David Villa, Fernando Torres of Chelsea, Athletic Bilbao's Fernando Llorente and Sevilla's Alvaro Negredo.
"We have to be intelligent against Chelsea in the final game," Soldado was quoted as saying on UEFA.com.
"It will be difficult. We can qualify with a 1-1 scoreline but we'll be going there to win and we are confident in our chances."
