Soldado, who is in the running for a place in the Spain squad at Euro 2012, pounced on a poor back-pass to net the opener after 41 minutes and struck a superb first-time shot after the break for the second.
He racked up his 15th of the campaign from the penalty spot after a handball from home defender Mikel San Jose, who also underhit the backpass in the first half.
Bilbao struggled to replicate the eye-catching form that helped them knock Manchester United out of the Europa League last week. They were missing injured striker Fernando Llorente and had defender Andoni Iraola sent off in the 66th minute.
Valencia moved on to 47 points with 11 left to play, 16 points behind second-placed Barcelona, who won 2-0 at Sevilla on Saturday.
Levante continued to defy predictions with a 1-0 victory at home to regional rivals Villarreal and climbed up to fourth with 41 points thanks to the 92nd-minute winner from Xavi Torres.
The result caused Villarreal to sack their coach Jose Molina, one point from their last five matches leaving them 17th with 27 points, three above the relegation places.
Bilbao were seventh with 37 points, one ahead of Atletico Madrid in ninth.
Ten-man Real Mallorca overcame Atletico 2-1 at home, the match turning in a crazy 10 minutes at the start of the second half.
Atletico's Diego Godin turned a shot into his own net in the 47th, Michael Pereira doubled the lead two minutes later and the islanders had defender Ivan Ramis sent off for handball in the 53rd.
Mallorca's Dudu Aouate saved the ensuing penalty from Radamel Falcao, though the Colombia striker responded with an outstanding lob to pull one back for the visitors in the 66th.
