Maatta's fourth goal of the season gave Pittsburgh its only lead as the Penguins won their 13th straight home game, a club record.
Alexander Ovechkin's 34th goal of the season gave Washington a 3-2 lead midway through the third period but the Capitals collapsed over the final 10 minutes. Brooks Laich and Jason Chimera also scored for Washington, which lost for the seventh time in nine games. Neuvirth made 33 stops, but didn't see Maatta's blast from the point with 1:54 left.
Pittsburgh extended its lead over the rest of the field in the Metropolitan Division to a whopping 18 points over Washington and Philadelphia by continuing to find a way to win at Consol Energy Center.
Over much of the first two periods it was difficult to tell which team was coming off a shootout loss in a different building the night before and which one was playing for the first time this week.
Washington has one of the game's top power plays, but Laich provided a short-handed tally when he took advantage of a turnover by Letang to ignite a two-on-two break that ended with Laich all alone in front of Fleury. A flick of Laich's wrist later the Penguins were trailing, a rarity during their run of home dominance.
Letang atoned 9:53 into the second period, ending a Pittsburgh rush by taking a deft drop pass from Sidney Crosby and throwing a puck at the net that deflected off two Capitals before sneaking by Neuvirth to tie it. Crosby's assist extended his home points streak to 17 games, the second-longest of his career.
Chimera put Washington back in front less than five minutes later, easily tapping in a centring pass from Marcus Johansson. Pittsburgh pulled even with 3:52 left in the second as Pyatt scored for the first time since April 23, 2013, when he was a fourth-line forward for the New York Rangers.
Maatta did the hard work, faking a shot from the point then skating around a fallen defender before setting Pyatt up in the left circle.
It set the stage for another frenetic finish for a rivalry that should be rekindled anew with the two teams back in the same division under the NHL's realignment.
Ovechkin put Washington back in front 8:35 into the third with a remarkable goal. He had his stick smacked out of his hands during a Washington rush then scrambled to pick it up just in time to receive a pass from Johansson. Fleury was no match for Ovechkin's wrist shot as the Capitals went in front for the third time.
And the last time. Brandon Sutter threaded a beautiful backhand pass through the crease to Jokinen for the Finnish Olympian's 13th goal of the year 11:35 into the third before Maatta, a 19-year-old rookie who also will play for Finland in Sochi, provided the most electric moment of his breakout season.
NOTES: The Penguins have won seven of the last eight meetings between the teams. ... Pittsburgh F Craig Adams played in his 254th straight game, tied for the fourth-longest streak in club history. ... Ovechkin has 23 goals in 33 regular-season games against Pittsburgh. ...