Luis Suarez (C) celebrates his late Barcelona winner against Rayo Vallecano with Gerard Piqué (L) and Munir El Haddadi at Campo de Fútbol de Vallecas in Madrid, Spain, on November 3, 2018.
GONZALO ARROYO MORENO/GETTY IMAGES
Barca looked set for a defeat when Jose Pozo and Alvaro Garcia cancelled out Suarez's early opener, FourFourTwo reported.
The Catalan giants produced a stirring comeback, though, with Ousmane Dembele drawing them level in the 87th minute before Suarez delivered the decisive blow three minutes later.
The Uruguay international has netted six times in his past four games, while he is La Liga's top scorer with nine.
Valverde said the former Liverpool forward, 31, was still at his peak.
"Luis Suarez has been playing at the top of his ability for a very long time," he told a news conference.
"Right now, he's scoring goals, more goals than perhaps before. We need him and we're extremely happy with him."