With the two biggest stars on the U.S. national team facing each other for the first time in six years, Danny Murphy put Fulham ahead at Goodison Park with a 14th-minute penalty kick that beat American goalkeeper Tim Howard.
Donovan's cross from the right flank was headed in by Denis Stracqualursi in the 27th minute for his first goal for Everton.
Again passing from the extreme right side, Donovan's cross was headed in by Marouane Fellaini in the 73rd minute.
"Landon's been great since he's been here," Everton assistant manager Steve Round said. "He's a real diamond of a guy. He's a very intelligent footballer and the lads all like him. You've seen the quality of his end product, whether it be from crosses or set plays. He's a top player."
Teammates on the past two U.S. World Cup teams, Donovan and Dempsey had not faced each other since May 6, 2006, when Dempsey's New England Revolution beat Donovan's Los Angeles Galaxy 4-0. This was only the seventh time overall they've played against each other.
Donovan was playing the sixth game of his second loan spell from the Galaxy to Everton. Dempsey has been with Fulham since 2007.
Dempsey, who had scored two hat tricks in his previous three games for Fulham, headed over the crossbar at the start of the second half following a cross by Bryan Ruiz.
Fulham had progressed in the FA Cup on all four previous occasions it had been drawn against Everton. The Cottagers were awarded the penalty kick after referee Howard Webb's handball call on John Heitinga.
In Friday's other fourth-round game, Tottenham won 1-0 at second-tier Watford on Rafael van der Vaart's 42nd-minute goal.
Manchester United is at Liverpool in one of 12 FA Cup matches Saturday, with the other two games scheduled for Sunday.