Los Che could not find the breakthrough at the Mestalla but nevertheless went through 2-0 on aggregate thanks to the two late goals they scored through Eduardo Vargas and Sofiane Feghouli in the first leg.
Valencia will now face surprise packages Ludogorets for a place in the quarter-finals, with the Bulgarian side having upset Lazio earlier on Thursday.
Dynamo were left with a mountain to climb after conceding twice in the last 11 minutes in Cyprus - where the first leg was played due to the serious unrest in the Ukrainian capital - but they looked up for the challenge early on in Spain as they earned a corner in the opening 30 seconds.
However, nothing came of that and Dynamo did not give their hosts much more to worry about until deep into the second half when Miguel Veloso rattled the Valencia crossbar with a long-range effort in the 75th minute.
Yevhen Khacheridi then sent a header over soon after while Ognjen Vukojevic also tried his luck from outside the box as Dynamo sought the goal that would have got them back into the tie.
There was no way through for the visitors though and 2004 UEFA Cup winners Valencia, who had chances of their own through Federico Cartabia, Dani Parejo and Vargas, sealed their berth in the next round.