As Brad Marchand approached Michal Neuvirth, the left wing couldn’t even get a shot on net because of the violence of Ivan Provorov’s hook. Patrice Bergeron’s power-play shot deflected off the stick of Andrew MacDonald.

The way the Bruins’ luck has run the season, the expectation would have been for neither puck to do damage.

But the Bruins scored a 6-3 decision over the Flyers at TD Garden on Saturday partly because their luck is changing. Even without snapping the puck on goal, Marchand scored an unassisted shorthanded goal at 7:48 of the first period after Neuvirth whiffed on the attempt. Bergeron scored the game-winning goal at 13:04 of the second when the puck caromed off MacDonald’s stick and tumbled over Neuvirth’s glove.

After half a season of high volume but little results, the Bruins’ goal-scoring fortune may be turning.

“You see some of the goals we’ve gotten lately — in St. Louis, we had one bounce off the boards, bounce off the goalie, and go in,’’ Marchand said of Brandon Carlo’s goal on Tuesday. “My goal tonight. But it all starts with how we’re playing. We’re playing great hockey. We’re giving ourselves lots of opportunities to score goals. Even in Nashville, the goalie made a ton of really good saves. We could have easily had 4-5 goals.

“Our team’s coming together right now. We’re all realizing how we have to play to win. We’re connecting well with each other. It shows we’re playing good hockey.’’

In the NHL, the best way to control your chances is to put the odds in your favor. The Bruins have done that consistently in terms of generating shots, possessing the puck, and accumulating scoring chances.

The Bruins are the best possession team in the league based on shot attempts. They’ve been good at turning their shots into chances. The trouble is that for most of the year, their hard work has not been rewarded.

The longer the season goes, however, the more likely that things regress to the mean. Expanded sample sizes produce clearer data. Pucks that don’t go in during limited windows find the back of the net in bigger brackets.

This could explain why a once-stagnant offense that depended too much on Tuukka Rask is looking like a collection of finishers. Torey Krug had one goal in his first 43 games. The defenseman now has a three-game goal-scoring streak after he converted Marchand’s cross-ice feed at 6:00 of the second period. Marchand (shorthanded, empty-netter) has seven goals in his last five games, reversing a 1-in-10 skid.

On the other hand, David Pastrnak hasn’t scored since Dec. 14 despite pounding six pucks on Neuvirth and assisting on two goals.

That’s hockey.

“It’s starting to come,’’ Krug said. “We can sense right now in our locker room that we’re on the verge of something right now. Hopefully we can string a couple wins together. You can see how dangerous our team is when our power play’s clicking, our penalty kill’s where it’s at, and Tuukks is seeing the puck the way he is. I don’t think many teams want to play us when we’re at our best.’’

The Bruins blitzed Neuvirth with 38 pucks. They had 14 others blocked and 14 more miss the target, including iron strikes by Frank Vatrano and Tim Schaller. The Bruins led the Flyers in attempts, 67-51, an accurate depiction of how they controlled the pace of play, especially in the second period.

With the score tied at 1-1 after 20 minutes, the Bruins pulled ahead with four strikes in the second: David Krejci’s power-play goal, Krug’s five-on-five score, Bergeron’s one-up tally during a five-minute Jakub Voracek boarding major, and Zdeno Chara’s even-strength one-timer. The Bruins buried 25 percent of their second-period shots, a measure not just of good luck, but also one reflecting a high percentage of quality scoring chances.

Even with a four-goal output, the Bruins had to slam the door. Wayne Simmonds scored a five-on-three goal with 3.2 ticks remaining in the second, closing the score to 5-3. Had the Flyers opened the third with another one-up goal during the remainder of Chara’s delay of game penalty, the outcome might have been different.

“That was, I think, a big key in the game,’’ said coach Claude Julien. “I talked to the guys about how important that kill was going to be at the beginning of the third. Certainly didn’t want to give them any life.’’

Julien had a tough job in the first half of the season. He had to remind his players to keep their heads up when the puck wasn’t going in. Julien knew the outcomes would improve if the team respected the process. Twenty-two goals in the last six games is proof that Julien was right.

“We know there was a lot of games we should have come out with points and we didn’t,’’ Julien said. “It wasn’t necessarily always because of our play, but maybe a bit more because of our finish.’’

Fluto Shinzawa can be reached at fshinzawa@globe.com. Follow him on Twitter @GlobeFluto.