Garri Kasparov of the Soviet Union moved into first place Sunday in the World Cup Chess Championship with a 10th round victory over Ulf Andersson of Sweden. He took over the lead from Joan Ehlvest of the Soviet Union, who lost to Anatoly Karpov, also of the Soviet Union. Ehlvest is in second place and Karpov in third. There were draws between Nigel Short of Britain and Alexandre Beliavski of Sweden, Arthur Youssoupov of the Soviet Union and Johan Hjartarson of Iceland and Jesus Nogueiras of Cuba and Boris Spassky of France. The three-week tournament, the second of six in the World Cup, will reward a total of $1.2 million in prize money to the winners. Sixteen grandmasters are competing in the tournament. Standings after Sunday's 10th round: 1. Garri Kasparov, USSR, 7.5 2. Joan Elvest, USSR, 7 3. Anatoly Karpov, USSR, 6 ( l adjounred) 4. Andrei Sokolov, USSR, 6 Boris Spassky, France 6 6. Robert Hubner, West Germany 5.5 ( l adjounred) 7. Zolan Ribli, Hungary, 5.5 8. Nigel Short, Britain, 5 9. Ulf Andersson, Sweden,4 Alexander Beliavski, Sweden, 4 Jonathan Speelman, Britain, 4 Arthur Yoiussoupov, USSR, 4 Johan Hjartson, Iceland, 4 14.Ljubomir Ljubojevic, Yugoslavia, 3.5 Jesus Nogueiras, Cuba, 4 Jan Timman, Netherlands, 4