Fulham, whose 11 game winless streak left it dangerously close to the relegation zone, climbed four points above the drop zone thanks to an inspired goal by Dempsey. The 24-year-old American zoomed through a crowd of Liverpool defenders, passed to Liam Rosenior on the wing, then slid into stroke the return pass into the net. It was Dempsey's first goal for Fulham.
Dempsey was 52nd minute sub in what was his ninth appearance, all off the bench, for Fulham since his arrival from New England in January. Defender Carlos Bocanegra went the full 90 and Brian McBride went 86 minutes for Fulham. A tie or loss by Charlton Monday against Tottenham will clinch Fulham's survival.
Tim Howard helped Everton to a 3-0 win over Portsmouth that puts it into a good position to earn a UEFA Cup spot. Blackburn (goalkeeper Brad Freidel, 90 min.) downed Newcastle (defender Oguchi Onyewu, 90 min.), 2-0, to keep its UEFA Cup hopes alive. Reading (goalkeeper Marcus Hahnemann, 90 min.) fell, 2-0 to relegated Watford but remains in seventh place and in the tight UEFA Cup race.
Jonathan Spector played the final 11 minutes for West Ham, whose 3-1 win pulled it out of the relegation zone.
DaMarcus Beasley started and went 61 minutes in Manchester City's derby loss on Saturday to Manchester United, which was crowned champion the next day.
In the second tier, Leeds (Lewis) finished last, was penalized 10 points for going into bankruptcy, and drops to the third tier next season.
In Mexico, Castillo, 19, who started and went 73 minutes, helped Santos Laguna to a 2-0 win over San Luis in the repechaje for a 2-1 aggregate win and spot in the quarterfinals. Another American, California Michael Orozco, 21, went the full 90 for San Luis. Santos faces Pachuca.
In Germany, Steve Cherundolo and Hannover 96 won their third straight game, a 2-0 win over Energie Cottbus, to keep its UEFA Cup hopes alive. Kamini Hill played the final 26 minutes for Wolfsburg in its 2-0 loss to Borussia Dortmund.