Less than two minutes into the first period, Pittsburgh was playing without its top two centers.
Boston goalie Tuukka Rask made 30 saves for his third shutout of the season.
The Bruins (36-22-10) have won five in a row and seven of their past eight to tie the Washington Capitals for the first wild card into the Stanley Cup Playoffs from the Eastern Conference, seven points ahead of the Ottawa Senators.
Crosby was a late scratch for unspecified reasons after participating in warm-ups. Penguins coach Mike Johnston was notified Crosby was not feeling well and was seeing doctors minutes before the game.
"It's just he wasn't feeling well. That's the best way to describe it," Johnston said. "So, it's not an injury. He didn't get himself injured in warm-up. He just wasn't feeling well and he went to see the doctors. I thought he was great at our meeting. He seemed to be fine, but somewhere between then and the end of warm-up when he came into the dressing room, he went to see the trainers and they said to see the doctors, and from there the decision was made that we were just going to keep him out."
Forward Craig Adams replaced Crosby 7:18 into the first period. Because Crosby was in the submitted lineups, the change had to be made according to Rule 7.1, which states changes to starting lineups must be reviewed and approved by the referee prior to the start of the game.
"I came to the rink, and about 40 seconds before the game started they let me know Sid couldn't go. So I just got dressed," Adams said. "It's not ideal, that's for sure. It's a little tough. I never did that before, but once I got a couple shifts, I felt OK."
Malkin seemed to sustain a lower-body injury after colliding with Bruins forward Chris Kelly during his first shift. He returned to the Penguins bench midway through the first period but was absent to start the second after playing 4:15.
Johnston said it is uncertain if Crosby or Malkin will be available against the Detroit Red Wings on Sunday (12:30 p.m. ET; NBC, SN), but said the Penguins "think they might be able to play."
Rask said he didn't notice Crosby wasn't playing until 15 minutes into the first period. Bruins coach Claude Julien, asked if he would be fine with Adams replacing Crosby, responded, "I know they missed a lot of good pieces, but at the end of the day, it's a team that comes and plays hard and they made a game of it.
"We played them well. It was a good, close contest. Tuukka was good for us and a big goal by [Milan Lucic] to give us that one-goal cushion there."
Lucic scored 9:53 into the first period; the Bruins have scored first in 11 straight games. Boston captain Zdeno Chara scored an empty-net goal from his zone with 37.7 seconds remaining.
Rask wasn't tested much in the third period, facing eight shots that had little chance of scoring, but he made an impressive glove save on Penguins defenseman Ian Cole at 8:43. After being set up by Rob Scuderi, Cole one-timed a slap shot aimed toward the upper-right corner of the net, but Rask used his glove to stop play.
Penguins goalie Thomas Greiss made 28 saves but took his fourth regulation loss in 16 games played (8-4-3).
Lucic scored after Penguins defenseman Ben Lovejoy blocked a David Pastrnak wrist shot that returned directly to its sender. Pastrnak gathered the puck a second time and set up Lucic between the faceoff circles, where he sent a wrist shot under Greiss' blocker.
"[Scoring first] is a huge difference," Lucic said. "If you look at the last bunch of games, being able to get that first goal and establish a lead, it takes a lot of pressure off of us and allows us to play our game, and we've done a good job getting the first goal of the game, and especially against a team like Pittsburgh, who comes at you real hard and real strong and tries to get that first one and build off that.
"So obviously, Tuukka did a great job in the first five minutes there, weather their storm and their push and we were able to get that first one and play a good defensive game and get a big win here today."
Pittsburgh had the better scoring chances in the second period and managed to get two shots past Rask that hit the left post.
Slightly more than one minute into the second, Spaling's wrist shot hit the post about 30 seconds after Blake Comeau was denied by Rask's left pad. Comeau seemed to have Rask beaten on a forehand-to-backhand deke that caused the goalie to fall forward.
The same post robbed Daniel Winnik with 7:49 remaining in the period. Bruins defenseman Dougie Hamilton's stick broke on an attempted slap shot that sent the Penguins charging into the Boston zone with a 3-on-1. Kris Letang fed Winnik, whose snap shot avoided Rask but did not go into the net.
"I don't think we gave them too many great scoring chances," Rask said. "They got a lot of rushes, mostly because of our own doing, but when we keep them outside and don't let them come back to the middle and stuff, it makes my job easier."