"It's nice to have some puck luck," said Lucic, who said both goals hit a Blue Jackets player and changed direction en route to the net.
The rugged Boston winger, who also had a fight in the second period, even thought linemate Jarome Iginla may have scored the second one.
"I thought Iggie may have gotten it," he said. "But it's nice to get two goals and my first power-play goal of the season."
Lucic hadn't scored a goal in his past six games after getting off to a fast start with nine.
Boston coach Claude Julien felt the winger just needed to relax and things would start to turn his way.
"I thought maybe he was gripping the stick a little tight in certain areas," Julien said. "I just told him to go out and play. I liked his game a lot tonight."
David Krejci added two assists for Eastern Conference-leading Boston, which is 10-2-2 in its past 14 games.
Johnson knew it was an easy night.
"The first period I didn't face many shots and in the second not many high-quality chances," he said. "It's tough to get into it, but I've had some good practices lately."
The Bruins haven't lost at home in regulation in 11 games (9-0-2). Boston has won all three meetings between the teams this season.
Ryan Johansen scored a power-play goal for the Blue Jackets, who were outshot 36-14.
Backup goaltender Curtis McElhinney stopped 33 shots for Columbus, which lost for the 12th time in 17 games. The Blue Jackets haven't won consecutive games since late October.
"It's definitely frustrating. I think some night that we have lost the effort wasn't there," winger Matt Calvert said. "But I thought tonight we worked hard, we did a lot of good things.
"But, once again, against a good team like this, you've got to find a way to win. It's always a tough building to come into, but we didn't find a way tonight and we're going to keep on searching for it."
Boston jumped ahead 1-0 when Bergeron scored on a tough-angle shot at 9:02 of the first. He fired one from near the right boards and the puck slipped behind McElhinney as Boston winger Loui Eriksson was cutting in front.
The Bruins made it 2-0 on Lucic's power-play goal with just over 5 minutes left in the first. Torey Krug fired a shot from the left point and Lucic, positioned in front, tipped it by McElhinney.
Lucic's second goal of the game made it 3-0 just over 2 minutes into the third. He fired a shot from the high slot and the puck popped into the air after McElhinney's stop and bounced into the net behind him just as Iginla was ready to bat it in.
Johansen's team-leading 10th goal came on a wrister from the top of right circle with just under 14 minutes left.
Coming off a 4-2 win over Edmonton at home on Friday night, the Blue Jackets had trouble generating much offense.
The Blue Jackets were outshot 9-2 in the first and it didn't get much better for them in the second. They were held to three shots on goal for nearly half of the period until a power play gave them a brief spark.
"Not enough (shots) and not enough quality ones either," forward R.J. Umberger said. "We've got to find a way to generate more."
Possibly looking to give his team a lift, Columbus' defenseman Dalton Prout took on Boston heavyweight Lucic for a fight midway into the second. Things were chippy, at times, for stretches in the second -- with a couple of scrums after whistles.
Columbus went nearly 18 minutes without a shot on goal from the first into the second -- and that was a clear from their own zone on one of Boston's power plays.
The Bruins posted a 3-2 victory over the New York Rangers on Friday.
The Bruins improved to 14-2-1 when scoring the game's first goal. ... Columbus' LW Nick Foligno was given an unsportsmanlike conduct minor and 10-minute misconduct late in the second after he grabbed Boston D Dennis Seidenberg by the jersey from behind and spun him around during a scrum at center ice. ... The Bruins are off until Thursday when they play rival Montreal. Columbus hosts Tampa Bay on Tuesday, the first of two straight at home. They also play Minnesota. ... The Blue Jackets fell to 1-11-0 when they trail after two periods. ... Former Bruin Johnny "The Chief" Bucyk watched the game from a luxury box. His No. 9 is retired and hanging in the rafters. ... A big melee broke out in the high-priced seats late in the game.