Real's title challenge appeared to be disappearing when they lost 2-0 to Barca last weekend but the champions' 0-0 draw at Espanyol on Saturday left the door ajar and Real grabbed the opportunity.
Gonzalo Higuain opened the scoring in the first half but it needed a second from Cristiano Ronaldo in the 77th minute to make sure of the win, as Valencia belatedly threatened to get back into the game.
"Barca are still top but we are now just one slip-up away," Real director general Jorge Valdano told Spanish television.
Valencia's timid start played into Real's hands and it came as no surprise when Argentina's Higuain spun past his marker to net his 25th of the campaign after 25 minutes.
The hosts should have made more of their dominance, but a flying save from Iker Casillas and Juan Mata's follow up against the post reminded Real of the slenderness of their lead.
Ronaldo's driving runs and Guti's passes continued to give Real the edge but a hushed Bernabeu reflected a growing nervousness.
Valencia's David Silva had been anonymous until he crashed a 25-metre drive against the crossbar midway through the second half and Portugal's Ronaldo settled the match firing in after good work down the left from Marcelo.
"Nino's not good, he's spectacular," Tenerife coach Jose Luis Oltra told reporters, of his forward who has netted 13 this season. "He's one of the best Spanish goalscorers around, especially as he does it with a team low down in the table."
