Anderson made 33 saves for the Senators, while Fleury stopped 31 shots.
"It was a little sloppy at times, but you've got to win them like that," said Neal. "It's going to be like that at times this year."
The Senators had an opportunity to win in regulation when Erik Karlsson's slap shot from the slot sailed just wide of Fleury with less than 40 seconds to play.
"The puck was bouncing a bit and I couldn't really settle it," Karlsson said. "I just tried to whack it and it didn't work out."
Jakob Silfverberg had a chance in overtime for the Senators, but after stealing the puck at his own blue-line from Chris Kunitz, he was tracked down on a breakaway by Ben Lovejoy before he was able to get a shot off.
Greening's first goal of the season for the Senators at 13:44 of the second came after miscues from both teams. Spezza had the puck in the Penguins' end and although his shot was stopped by Fleury, Greening was there for the rebound and he tucked it in from along the goal line.
"I really enjoyed the game and I feel everyone played well," Senators coach Paul MacLean said. "We got a point out of the game which is real important and we played well enough that we deserved a point and we were pleased with how we were able to be consistent throughout the game.
"I thought the game was very well played by both teams, we traded some opportunities here and there and I thought both goalies played well."
Neal's one-timer at 13:31 came after a cross-ice pass from Malkin, who has five assists this season.
Anderson has played 298 career games in the NHL and should play No. 300 at home against the Montreal Canadiens Wednesday. ... Malkin's first-period assist tied him with Rick Kehoe for seventh place on the franchise's all-time assist list with 324.
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OTTAWA, CANADA - JANUARY 27: Craig Anderson #41 of the Ottawa Senators looks on during warmup prior to a game...