Pittsburgh's 19-year-old superstar was covered by defensemen Anton Volchenkov and Chris Phillips throughout the series and the Penguins' power play went 0-for-6 Thursday to finish with no goals in its last 17 opportunities.
"We got beat by a great hockey team that's got a chance to win the Stanley Cup," Penguins coach Michel Therrien said.
Senators captain Daniel Alfredsson praised Crosby's effort in the series, which marked the prodigy's playoff debut.
"He played really well," said Alfredsson, who set up Heatley's power-play goal early in the second. "Obviously we do pay attention when he's on the ice all the time. We knew we wanted Volchenkov and Phillips out against him and we didn't give him too much room, especially the last two games. He's one heck of a player, there's no question."
Emery helped Ottawa weather two early 5-on-3s, including one that lasted 1:14 after Dean McAmmond was given a delay of game minor for backhanding the puck over the glass with Wade Redden already in the penalty box.
"Ray Emery was tremendous," Vermette said. "He made some big saves at key moments and then we took over and built some momentum. That was huge for us tonight."
Heatley scored his second goal of the series on a power play 1:08 into the second and Vermette made it 2-0 when he drove through the slot and scored on Marc-Andre Fleury.
Kelly brought the sellout crowd to its feet with a roar once again when he beat Fleury at 17:55.
Ottawa, which has never squandered a 3-1 series lead, advances to face one of the three teams in the New York area.
"I thought we stuck to the game plan for pretty much every game, really executed well and came out of it with not a lot of injuries," Emery said. "We're pretty healthy."
The fourth-seeded Senators will either travel to No. 2 New Jersey, or host the sixth-seeded New York Rangers or the eighth-seeded New York Islanders when the second round begins.
Crosby, who turns 20 on Aug. 7, had three goals and two assists through the first three games of the series. The league's youngest scoring leader ever with 120 points this season, Crosby totaled 222 points in his first two seasons with Pittsburgh.
"It was obviously a tough finish but I think we exceeded a lot of expectations in the regular season and we'll have to learn from this," Crosby said.
With a youthful lineup that included Fleury, rookie of the year favorite Evgeni Malkin, 18-year-old Jordan Staal and promising defenseman Ryan Whitney, the Penguins finished a surprising fifth in the Eastern Conference with 105 points, the second-highest season total in franchise history.
Bolstered by veterans Mark Recchi, Gary Roberts and Sergei Gonchar, Pittsburgh returned to the playoffs for the first time since 2001 -- and ran into a Senators squad making its 10th straight run at the Stanley Cup.
"We had a fun year and we've really grown a lot together and had a great attitude all year," said Recchi, won won his second Stanley Cup last season with Carolina. "This is a great learning process for us right now and I think the guys will remember this feeling for the summer and for next year when the playoffs start. We had 14 or 15 guys playing their first playoff round and next year it's not going to be so foreign to them."
The Penguins had three straight power plays to begin the game. Ottawa was penalized twice for delaying the game within the first 3:32 after Christoph Schubert repeated McAmmond's mistake by clearing a puck over the glass in his zone.
Outshot 7-0 midway through the first period, Ottawa recovered to close out the period with a 9-8 shots deficit before taking it to the Penguins by a 12-6 margin in the decisive second period.
Heatley opened the scoring on the Senators' third power play of the game. He took Daniel Alfredsson's pass and beat Fleury with a shot from the edge of the crease.
Vermette connected shortly after Ottawa finished killing Pittsburgh's fourth power play, beating Fleury as he crashed into the goalie.
Kelly made it 3-0 and Mike Comrie came close to putting the Senators up by four when he drove a slap shot off the right post with 1:15 remaining in the second period.
- Penguins C Erik Christensen and RW Georges Laraque returned to the lineup. RWs Ronald Petrovicky and Nils Ekman joined Ds Joel Kwiatkowski and Alain Nasreddine and C Chris Thorburn as healthy scratches.
- Senators RW Patrick Eaves remained out of the lineup and is still recovering from Colby Armstrong's check which knocked him out of Game 3 with an undisclosed head injury.