Anderson was solid but it was Spezza's goal that highlighted the fortunes of two teams heading in opposite directions.
The forward gave Ottawa a 3-0 lead 2 minutes into the second period on a crafty one-man effort in which he used every inch of his 6-foot-3 frame to end Johnson's night early.
Spezza broke in alone and drew the goalie all the way out of the net with a series of feints. Spezza then skated around the sprawled netminder and appeared to be heading behind the net for a wraparound attempt, only to cut back behind Johnson and clang the puck off the far post.
"I just got (Johnson) to bite on the fake and got around him and just used my reach to kind of tuck it in," Spezza said.
His teammates were a little more effusive.
"He did some pretty sick moves out there," said Colin Greening, credited with the first of his career-high three assists on the goal "He didn't have much room to move, especially when he deked out Johnson, so he's got great hands and he showed it tonight."
Evgeni Malkin scored his 17th goal of the season for Pittsburgh but couldn't stop the Penguins from dropping their fifth straight. Johnson made just five saves on eight shots before being pulled early in the second period in favor of Marc-Andre Fleury.
Pittsburgh, a Stanley Cup favorite after Sidney Crosby's brief return in November, is eighth in the Eastern Conference at the season's midway point.
"When you lose that many in a row, it's tough, but you've got to find a way to battle back and get back to where we were as a hockey team," said Pittsburgh forward James Neal, who played despite a bruised foot. "Every game is crucial, but tonight was a crucial game and we came out and put ourselves in a hole right away."
While Pittsburgh is sliding, the Senators are surging. Ottawa has risen through the standings with a flair for the dramatic. The Senators lead the NHL in third-period comebacks, the last coming in a 6-4 win against Philadelphia on Sunday.
The fireworks came earlier against punchless Pittsburgh.
The Penguins started Johnson in net to give Fleury the night off before a trip to Washington on Wednesday. Johnson, stellar a year ago, has struggled this season. He came in with a 3.24 goals-against average and a mediocre .885 save percentage.
Both took a hit during a nightmarish night even though the Senators were playing without defenseman Erik Karlsson, scratched moments before the opening faceoff with an upper body injury.
Ottawa hardly needed the league's top-scoring defenseman, pouncing on the Penguins after surviving an early flurry.
Pittsburgh has made a habit of playing well early in games before falling off in the final 20 minutes. The collapse came much earlier this time.
Neil got Ottawa started, taking a feed from Kyle Turris and beating Johnson easily to put the Senators up 1-0 just over midway through the first period. Butler made it 2-0 less than 3 minutes later, taking a pretty feed from Nick Foligno and tapping it into a wide-open net.
Spezza's goal sent Johnson to the bench with a chorus of boos, though Fleury's luck was no better.
Ottawa scored on its first shot against Fleury, with the puck deflecting off Michalek's skate and into the net. It appeared Michalek moved his right foot to touch the puck, but officials ruled it a good goal to make it 4-0.
"A couple breakdowns and a couple miscues and we gave them goals, gave them easy goals," Pittsburgh coach Dan Bylsma said. "When they score four goals on nine shots, there's some serious gaps on our part."
Malkin gave Pittsburgh a flicker of hope by stuffing the puck past Anderson to score his 15th goal in 23 career games against the Senators.
But that was all the offense the Penguins could muster, and Pittsburgh has its first five-game regulation losing streak since the 2009-10 season.
The Penguins have scored just six goals during the skid as injuries have mounted quickly.
Crosby remains sidelined with concussion-like symptoms as does defenseman Kris Letang. Pittsburgh center Jordan Staal is out four to six weeks, though the team received some good news early Tuesday when Neal revealed his foot -- originally thought to be broken -- was instead just bruised.
Bylsma offered little update on Crosby or Letang, though Letang has skated several times in the last few days and could return to practice soon. Crosby is doing "light exercise" but hasn't progressed to the next stage of his rehab.
Former Stanford quarterback and likely No. 1 NFL draft pick Andrew Luck watched the game with his father, West Virginia athletic director Oliver Luck, as a guest of Penguins owner Mario Lemieux. ... The Senators travel to New York on Thursday. ... Defenseman Paul Martin and forwards Steve MacIntyre and Colin McDonald were scratched by the Penguins. ... Pittsburgh is 16-14-3 without Crosby this season.
Copyright by STATS LLC and The Associated Press
Arena: CONSOL Energy Center Location: Pittsburgh, Pennsylvania
Referees: Steve Kozari, Justin St. Pierre Linesmen: Derek Amell, Mike Cvik
Attendance: 18,603 (102.9% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Chris Neil (7)
Assists: Kyle Turris, Nick Foligno
Bobby Butler (5)
Assist: Nick Foligno
Jason Spezza (16)
Assists: Colin Greening, Chris Phillips
Milan Michalek (21)
(Power Play) Assists: Colin Greening, Jason Spezza
Evgeni Malkin (17)
Milan Michalek (22)
Assists: Colin Greening, Filip Kuba