Michael Owen's first-half goal gave Liverpool an away victory in the UEFA Cup third round, first leg in Holland.
But the England striker missed three other gilt-edged chances when clean through which would have given Liverpool a comfortable lead.
Instead they were on the backfoot for most of the second-half as they looked to cure themselves of a Champion's League hangover.
Next it was Smicer's turn to be played in, but again Jevric produced a fine save at his feet.
Claessens headed over from Rahamat Mustapha's cross and the game was on a knife-edge with Liverpool escaping on the break but Vitesse searching for the equaliser.
Heskey came on for Baros after 74 minutes, with the home side throwing on Kalle Sone and Eldridge Rojer for Frankel and Mbamba three minutes later.
Eight minutes from time Liverpool somehow survived when Mustapha hit the post and Sone found himself with an open net to roll the ball into - but somehow contrived to miss from six yards.
Dudek made another excellent save from Claessens from close range in injury-time as Liverpool held on to their slim first-leg advantage.