The two teams appeared to be settling with a draw when Carew's goal -- his third in the current season -- silenced a home crowd of 31,000.
``Valencia was lucky. They did not deserve victory,'' Roma's Cafu said after the match. ``Carew's strange goal put us on our knees. We must win the next match to keep our hopes alive. A victory would also boost our morale.''
Roma, which is doing poorly also in the Italian league and is out of contention for the title, had to start a weakened team following injuries which sidelined its imaginative captain Francesco Totti and French defender Vincent Candela.
In Barcelona, Inter had Uruguayan international forward Alvaro Recoba ejected in the closing stages during its first defeat of the second phase.
Barcelona's landmark Champions League win was again in stark contrast to its performances in the Spanish league, which recently cost coach Louis Van Gaal and club president Joan Gaspart their jobs.
Barcelona gave van Gaal's replacement, Serbian coach Radomir Antic, a marvelous start to his first European match in charge when Saviola crashed the ball home in the seventh minute from a precise pass by midfielder Xavi Hernandez.
Cocu then scored in the 29th against the run of play, before Saviola set up Kluivert in the 68th minute.
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