The sellout crowd chanted the 29-year-old Spezza's name during his first shift.
Spezza faced a familiar opponent. His last game before surgery was at home against the Penguins, when he earned one assist and logged 21 minutes of ice time.
In his first game back, Spezza was slow to backcheck but he managed to generate a few scoring chances and made nice passes.
His back was put to the test in overtime when Penguins forward Craig Adams delivered a bone-crunching hit along the boards. Spezza shook off the check.
"I popped up as quick as possible and tried to get to the bench," Spezza said. "I was just trying to get the puck out and was in a vulnerable position, and he picked me a little clean there."
Pittsburgh's best scoring opportunity in the overtimes came when Pascal Dupuis hit the post with a drive during the first extra session.
"We had some better chances that we didn't put in tonight," Jarome Iginla said. "I thought for ourselves, we weren't as sharp, but give them credit."
Anderson was on his game after being pulled in Game 2. He robbed Crosby early in the second period, and moments later stopped a hard shot by Evgeni Malkin, who smashed his stick against the ice in frustration.
He again stymied Malkin with a sprawling save in the first overtime. Anderson's effort brought the crowd of 20,500 to its feet with chants of "Andy! Andy!"
"You just want to give your team a chance to win," Anderson said. "Sometimes stats are misleading. You just kind of build off the good stuff."
Senators defenseman Erik Karlsson took a slashing penalty with less than two minutes left in the game, but Ottawa not only killed it, but got the tying goal from Alfredsson.
"That's why he's been the captain for so long," Karlsson said. "He never quits and he leads the way for the rest of us. He showed that even though we were down a man we were really going to try and win the game and that's exactly what he did."
NOTES: Ottawa improved to 3-0 at home in this postseason. ... The Senators took seven penalties against the Penguins, who own the top power-play unit in the playoffs, but didn't allow a goal.