Goals by Paco Alcacer - benefiting from a terrible error by Kuban goalkeeper Aleksandr Belenov - and Sofiane Feghouli saw Miroslav Djukic's troops get on track in Group A following their humiliating 3-0 defeat at the hands of Swansea on matchday one.
The Swansea result came amid a dismal run of form in the Primera Division that saw Djukic's job come under threat, but the coach has cajoled a fine response from his players, with Thursday's win coming after three straight La Liga victories.
Kuban - who lost 2-0 to St Gallen last time out - never got into their stride over the whole 90 minutes and their only clear-cut chance of the contest came midway through the first half when Djibril Cisse worked space but dragged his shot wide.
Valencia's only threat in the first period came on 25 minutes when Sergio Canales' corner was met with a firm header by Feghouli but Belenov made a decent save.
Sadly for Belenov that good moment would not be his abiding memory of the match as with 17 minutes remaining it was his awful blunder that gifted Valencia the opener.
Rushing from his area to deal with a long ball downfield, Belenov appeared to get caught in two minds over whether to kick or head the ball and did neither, instead falling comically to the floor to allow the disbelieving Alcacer to run through and score.
And Belenov was far from blameless for Valencia's second with nine minutes remaining, allowing Feghouli's bouncing free-kick to beat him in the left corner.