Neal scored in regulation and in the shootout as the Penguins defeated the Ottawa Senators 2-1.
"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."
Sidney Crosby and Evgeni Malkin, with the winner, also scored in the shootout for Pittsburgh (4-2-0), which snapped a two-game skid. Marc-Andre Fleury made 31 saves for the win.
"We obviously didn't want to keep sliding," said Crosby. "Every game is so important. It wasn't a pretty one but it was good we were able to find a way."
Colin Greening scored a second-period goal for the Senators (3-2-1), while Jason Spezza and Kyle Turris collected shootout goals after Fleury stopped Milan Michalek with the first attempt.
"Fleury was big for us tonight," said Neal.
Craig Anderson turned aside 33 of 34 shots and has allowed just three regulation goals through four games so far this season.
The Senators had a golden 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 getting a shot off.
"The pace picked up at the end and both teams really tried to win the game, said Karlsson. "That's what hockey is about — no team played to lose and both teams were going for it and trying to create chances. It was a tricky game."
The pace was slower through the first 50 minutes but the tempo did pick up over the final 15 minutes.
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," said Senators head coach Paul MacLean. "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."
That was the only real miscue the Penguins had all game.
"We wanted to make a conscious effort against the (Senators) to limit scoring chances," Penguins defenceman Brroks Orpik said.
"Goals against is something we've struggled with in the first four games this year, and against the Senators last year. It was a good win. We did give up some chances, but (Fleury) was great for us."
Neal's one-timer at 13:31 came after a cross-ice pass from Malkin, who has five assists this season.
The Senators now have two straight losses after opening the season with three wins. They do have seven points however, which are points that will be very useful down the stretch.
"We should be happy where we are but we can't be satisfied," said Karlsson. "We have to keep building on what we have collecting points and hopefully don't give any away."
The Senators are off Monday but host the Washington Capitals Tuesday and Montreal Canadiens Wednesday.
The Penguins are home to the Islanders Tuesday.
Notes: Dustin Jeffrey, Robert Bortuzzo and Simon Despres were scratches for the Penguins. ... Daniel Alfredsson and Patrick Wiercioch were scratches for the Senators. ... Senators goaltender Craig 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.