Nielsen, who centers the Islanders' second line and plays on both special teams, left Game 5 on Thursday with a lower-body injury and didn't skate Friday.
Nelson took part in the morning skate and was expected to play if Nielsen was unable to go; but both players skated in pregame warm-ups and were in the lineup
Nelson, the 30th player taken in the 2010 NHL Draft, had 25 goals and 52 points for the Bridgeport Sound Tigers, the Islanders’ American Hockey League affiliate, in his first professional season.
The previous Islanders player to make his NHL debut in the Stanley Cup Playoffs was Trent Hunter in 2002.
Nelson was the 30th player taken in the 2010 NHL Draft.
"From training camp until now he's put on about 15 pounds," Capuano said. "He's much stronger. Twenty-five goals, 27 assists, 52 points down there this year -- he was one of their top players."
Capuano said he isn't worried about throwing Nelson into the playoffs.
"We have the utmost confidence in the guys we play," the coach said. "If Brock does get in there, I've said it before: We wouldn't put anyone in that we didn't feel was ready. We feel that he is ready to play."