The Penguins, seeded No. 1 in the conference, finished off the Senators in five games and warmed up for the next round by scoring 13 goals over the final two contests of the semifinals.
Pittsburgh will take on either Boston or the New York Rangers for the right to move on to the Stanley Cup Finals. Boston holds a 3-1 lead over the Rangers and the Bruins will host Game 5 of that series on Saturday.
Brenden Morrow scored on a deflection 6:25 into the game to give the Penguins the lead, but that was the only goal of the opening period.
Malkin's goal was the backbreaker, coming with just 30 seconds left in the period after Ottawa had given itself some hope when Milan Michalek cut the Senators' deficit to two.
Neal scored twice in the third period to run his playoff goal total this season to six.
Tomas Vokoun made 29 saves to win for the sixth time in seven starts since taking over for an ineffective Marc-Andre Fleury. The goaltender change came during the opening-round series against the New York Islanders.
Pittsburgh's offense has come to life as well. The Penguins outscored the Senators in the series 22-11.
Ottawa's lone win in the series was a double-overtime decision in Game 3.
All of Pittsburgh's goals Friday came against Craig Anderson, who made 27 saves.