Also, NEC Nijmegen continued its good form with a 1-0 win over Roda Kerkrade to move into fourth place on 27 points; while Ajax beat Vitesse Arnhem 2-0 to go into sixth place with 24 points.
At Rotterdam, Kuyt took advantage of a weak clearance by PSV goalkeeper Gomes to slot home.
Feyenoord dominated the match with darting runs from Salomon Kalou proving a handful to PSV.
Jefferson Farfan wasted four chances in the first half for PSV. The Peru forward failed to capitalize on a mix-up in the Feyenoord defense by shooting wide in the 26th minute.
Five minutes later, Farfan's weak header was cleared by Feyenoord defender Pascal Bosschaart.
"In the first half, we created a lot of chances," PSV coach Guus Hiddink said. "We also took control of the game, but we failed to score."
At Arnhem, captain Tomas Galasek scored a first-half penalty and Angelos Charisteas converted on a pass from Markus Rosenberg in the 75th.
Also Sunday, FC Utrecht played its first game since 26-year-old defender David di Tommaso died in his sleep on Nov. 28, losing 2-0 to FC Groningen; and RKC Waalwijk beat Sparta Rotterdam 3-2.
Former Swedish international Hakan Mild played his last game when IFK Goteborg lost 3-1 to Norway's Lyn in the Royal League.
Mild, a 33-year-old midfielder, played 458 games for Goteborg since 1987. He also had stints with Servette, Real Sociedad and Wimbledon.
In 1994, he was a member of the Swedish team that finished third in the World Cup in the US. He played 74 games for Sweden.
When Mild trotted off the field many of the 6,000 fans gave him a standing ovation, singing "We love you Hakan" and "Stand up for Hakan Mild."
"It was fantastic," said Mild, who will take an office job with the former two-time UEFA Cup champion.
Jo Tessem had two goals for Lyn. Stefan Gislason also scored for the Norwegians. Karl Svensson gave Goteborg an early lead.
Djurgarden of Stockholm, which was idle, leads Group 3 with six points on better goal difference than Lyn. Goteborg has four points and Aalborg of Denmark has one.
In Group 2, Espen Sogard scored a late goal to give Norway's Lillestrom a 1-0 away win over Brondby of Denmark.
Kalmar edged RL champion FC Copenhagen 1-0 at home in the other Group 3 match with Brazilian Cesar Santin getting the game-winner just before halftime.
Lillestrom tops the group with eight points, while Kalmar has five. Brondby and Copenhagen have two points each.
Start and Valerenga drew 3-3 in an all-Norwegian Group 1 game. Stefan Barlin had two goals for Start. Morten Berre also scored two for Valerenga. Glenn Andersen saved a point for Valerenga by getting the equalizer in the 89th minute.
Valerenga leads the group with five points, one ahead of Midtjylland of Denmark and Hammarby of Sweden, who meet today in Stockholm. Start has two points.
The Royal League involves the top four teams from Sweden, Denmark and Norway.
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