All of the scoring came in the final 20:04.
Lucic scored on a power play at 15:46 of the third period, when he tipped a shot over Stars goalie Kari Lehtonen for a 3-1 lead.
Lucic passed from the right corner to David Krejci, whose goal gave Boston a 1-0 lead at 19:56 of the second period. Krejci also had a goal and an assist.
In losing for the seventh time in eight games, Dallas dropped to 21-19-7. All seven losses have been against Eastern Conference teams.
The Bruins had a better chance to score some 11 minutes later. Boston was short-handed, but Brad Marchand had a breakaway. Lehtonen made a pad save.
Dallas appeared to score from a scramble at 18:09 of the first, but a referee said he had blown his whistle before the puck crossed the goal line.
Campbell had another chance on a short-handed 2-on-1 rush, but the Stars' Erik Cole hustled back to hit Campbell's stick as he shot. During that power play, Dallas had a 5-on-3 advantage for the last 35 seconds of the first period but couldn't score.
The period ended scoreless, but the Stars had an 11-6 advantage in shots on goal.
Boston took the upper hand in the second, with 11 of the first 12 shots.
The game was stopped a short time later when Boston's Zdeno Chara inadvertently hit Johnson with a stick. Blood flowed from a cut near his left eye, but the goalie stayed in the game after receiving medical attention.
Krejci ended the scoreless tie with just 4 seconds remaining in the second on a shot from the right circle.
NOTES: The Bruins and Stars have completed their season series. Dallas won the game at Boston in a 3-2 shootout to finish 1-1; Boston was 1-0-1. ... Stars assistant coach James Patrick missed the game because of his father's death. Stephen Patrick played for the Canadian Football League's Winnipeg Blue Bombers. ... Tennis player John Isner, who retired from his first-round match at the Australian Open, attended the game.