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 game as they looked to cure themselves of a Champions League hangover.
Manager Gerard Houllier rested several players ahead of Sunday's showdown with Manchester United as his side ventured reluctantly into the UEFA Cup third round.
Out went Dietmar Hamann, Emile Heskey, Jamie Carragher and John Arne Riise - and only the latter could consider he was suffering because of poor form.
The surprise was Stephane Henchoz returning in central defence after just 45 minutes' action in eight weeks following his calf operation.
Bruno Cheyrou and Salif Diao were given their chances in midfield while Milan Baros partnered Michael Owen up front, a reward for six goals in 15 appearances this season, mostly from the bench.
On eight minutes Cheyrou limped off the pitch with what looked like a hamstring injury, and Vladimir Smicer was sent into the fray.
Liverpool's midfield looked unbalanced. Steven Gerrard, making his first start since being publicly rebuked by Houllier, was operating on the right with Smicer playing in an advanced role. It left a gaping hole in front of Diao, who had acres of space to cope with.
Baros' sliced header from Murphy's corner was the nearest Liverpool came to scoring in the opening exchanges.
Gerrard showed something of his former self with a surging run at the heart of the home defence before being bundled down by Evgeniy Levchenko.
After 32 minutes Liverpool struck with a goal of real class. Smicer bravely won possession in midfield, Gerrard found Owen who pushed the ball back to his England teammate and scuttled off towards the box.
Gerrard's ball in was controlled and shielded expertly by Baros, who then rolled the ball into Owen's path for the striker to slot home from eight yards.
It could have been two after 34 minutes when another accomplished passing move ended with Owen retrieving the ball from the byline, tricking Tim Cornelisse and laying the ball back for Murphy to fire over from 12 yards.
A minute later Murphy stole in as a free-kick dropped into the box and sent a neat looping header agonisingly onto the roof of the net.
Liverpool were exposing Vitesse, and from another move involving Owen, Baros and Murphy, Gerrard powered a 25-yard dipping shot over the crossbar.
Just as in the first half, Vitesse started the second period quicker to the ball. One lofted cross into the box forced Djimi Traore into a high, looping header which Jerzy Dudek had to pull down from beneath his own bar.
However, Vitesse were getting closer to an equaliser, with Frankel and Emile Mbamba both getting clear shooting chances but failing to hit the target.
Liverpool broke in the 66th minute and again Owen should have scored. Baros got away and found the England striker racing through the middle.
Jevric saved his first effort but could only sit on the ground and pray as Owen's follow-up effort crept an inch wide of an open goal.
It got worse for Owen after 68 minutes when he was through on goal again - but saw Jevric save again. In the ensuing scramble Gerrard's chip towards an empty net was headed away by Stefanovic.
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
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