The Bruins swept the Penguins in the Eastern Conference championship series with Rask giving up just two goals in the four games.
Boston will try for its second Stanley Cup title in three years when it takes on either Chicago or the defending NHL champion Los Angeles Kings. Chicago will own a 3-1 lead over the Kings heading into Game 5 of the Western Conference finals on Saturday.
The only goal of Friday's series clincher came from Adam McQuaid 5:01 deep in the third period.
Rask took care of the rest, just as he had done in the first three games against the Penguins. He stopped 134-of-136 shots over 275 minutes, 19 seconds in the conference finals and improved his playoff record this year to 12-4.
Tomas Vokoun made 23 saves for the Penguins in what was his 11th straight start in these playoffs. He came in to replace a struggling Marc-Andre Fleury after five games of Pittsburgh's opening-round series against the New York Islanders and won six out of seven games to get the Penguins into the conference finals.