This win took them to within a point of third-placed Atlético, who later drew 0-0 at Sevilla, and who Valencia face next week.
Results: Getafe 1-1 Córdoba, Valencia 3-1 Atlético, Rayo 0-2 BarcEibar, Eibar 3-3 LevAlmeríalmería 2-2 Elche, Málaga 2-1 Granada, Sevilla 4-1 DEspanyol, Espanyol 2-2 Real Sociedad, Real Madrid 5-0 Espanyol.
Formally, Valencia still have a €230m debt and face a significant challenge to finish the new stadium, if they do ultimately do so, and sell the old one.
Valencia were forced to field a makeshift defence with the centre-backs Adil Rami and Ricardo Costa both injured, as well as the full-back João Pereira who was ruled out after picking up a hamstring injury during training on Tuesday.
Ancelotti added weight to his frontline by replacing the midfielder Thiago Motta with Gameiro and the newcomer's tricky dribble caused enough confusion in the Valencia defence to allow Lavezzi to finish.
That result came after Deportivo had stunned Valencia.
Results: Zaragoza 3-1 Osasuna, Celta 2-1 Getafe, Betis 1-0 Espanyol Barcelona 2-0 Granada, Mallorca 2-0 VaLevante Levante 2-1 Real Sociedad, Atlético 2-1 VAthleticd, Athletic 0-0 Málaga, Rayo-Real Madrid, postponed.
"Nicolás is happy at Valencia and with the fans but he's got an option to improve on a professional level.
By the final whistle, Valencia had taken 19 shots to la Real's eight.
Only Atlético have been as good as Valencia at home this season; they've won 11, drawn one and lost just one, and that was in the last minute against Barcelona.
But could Valencia aspire to more, Moyes was asked.
