Jerry Hairston Jr. replaced Swisher in right and was batting seventh. Hairston is 10 for 27 in his career against Phillies starter Pedro Martinez, but hasn't faced him since 2004.
"He's had a lot of success off of Pedro," Girardi said. "We also like the way they kind of match up against each other, and that kind of shows up in the numbers."
Swisher went 0 for 3 in New York's 6-1 loss in Wednesday night's World Series opener. He is batting .114, with no homers and 12 strikeouts in the postseason.
Swisher acknowledged he was shocked by the move.
"This is Skip's thing, and I'm behind him just like I'm behind everybody else on this team," he said. "We've got to get ourselves a win."
Hairston had appeared in just three career playoff games -- all this year -- and was making his first start in right since July 21.
"You always want to contribute," he said. "I've faced Pedro an awful lot. He's been a great pitcher for a long time."
Molina also replaced Jorge Posada behind the plate. Molina has caught each of Burnett's starts in the playoffs.
Phillies manager Charlie Manuel said Greg Dobbs and Stairs were in the mix for DH, but Dobbs was sent home to Philadelphia because he has the flu. Stairs also has two homers in 11 career at-bats against Burnett.