The Bruins (25-10-2) blew the game open early in the third period with two power-play goals 49 seconds apart after Craig Smith had cut Boston's lead to 3-2 with his second goal of the game at 3:25.
The Bruins' win was coach Claude Julien's 400th NHL victory.
"Right now, you hope as a coach that there's lots more ahead for you," he said.
Iginla batted his second goal of the game out of midair during a 5-on-3 advantage to put Boston up 4-2 at 5:01. Carl Soderberg's snap shot during a 5-on-4 advantage at 5:50 put the game out of reach.
Brad Marchand's eighth goal of the season with a little more than four minutes to play rounded out the scoring.
The Predators (16-17-4) had all the momentum following Smith's third-period goal, his 10th of the season, but Boston capitalized on back-to-back penalty calls against Nashville -- a bench minor at 4:21 for too many men on the ice, followed by a cross-checking penalty against Paul Gaustad at 4:44.
"We take two untimely penalties. That basically … Boston was not going to let you back there. It just killed our momentum," Predators coach Barry Trotz said. "That's my frustration, is that we've got a lot of guys really committed, really working, showing true character, and then we do things that can't happen, unacceptable things."
It was the third time the Predators have been called for too many men on the ice their past four games.
"We clawed ourselves back in it … then we just got into penalty trouble. We killed ourselves, kind of killed the momentum," Nashville forward Mike Fisher said. "The crowd was starting to get back into it, and we just let [the Bruins] back into it. It was our doing."
Trotz pulled Hutton in favor of Marek Mazanec before the game was six minutes old after Matt Fraser scored when Hutton mishandled Soderberg's dump-in from center ice. The puck went off Hutton and right to Fraser, who beat the Predators goalie high to his glove side.
Hutton allowed two goals on four shots; Mazanec stopped 25 of 29.
"I saw the second goal, and I saw enough," Trotz said.
It was Fraser's first goal with the Bruins after he was acquired as part of the offseason trade that sent Tyler Seguin to the Dallas Stars.
Reilly Smith scored on the power play to add to the Boston lead at 10:47. With Nashville defenseman Seth Jones in the penalty box on a hooking call, Smith fired a wrist shot past Mazanec from the bottom of the left circle. It was his 12th goal of the season.
Soderberg and Smith each had a goal and two assists for the Bruins, who return to action Friday at TD Garden for the opener of a home-and-home against the Ottawa Senators.
"There is depth in this organization," Smith said. "A lot of teams may have looked past us in the last few games because we have so many guys who aren't regulars on the roster, like Spooner and Fraser."
"Nashville had a lot of chances, especially in the third period," Rask said. "This was a great way for us to go into the break."
Nashville got on the board at 11:35 of the second when Smith scored with eight seconds left on a hooking penalty against Bruins forward Patrice Bergeron. Smith slammed in a rebound of Jones' slap shot from the left circle.
Material from wire services and team media was used in this report.