BOSTON — It can take a few weeks, or even a few months, for an NBA player to discover his role when joining a new team.

But that hasn’t been the case with Boston’s newcomers — Rasheed Wallace, Marquis Daniels and Shelden Williams.

The three have fit right in, and the Celtics’ bench is deeper than ever. Or at least it will be when Glen Davis returns from a broken thumb.

It was evident in Tuesday’s game against Philadelphia how important Boston’s newcomers are to the team.

In that game, a 105-74 Celtics romp, the starters got off to a slow start and Boston trailed, 10-4, in the opening seven minutes. Looking for a spark, coach Doc Rivers inserted Wallace, Daniels and Williams into the lineup, and they delivered.

The Celtics closed the first quarter with a 15-7 run over a four-minute span, and extended that surge to 29-11 over the opening minutes of the second quarter with four of Boston’s bench players in the game.

Wallace scored 11 points during the run and finished with 20 overall as Boston’s bench accounted for 59.6 percent of the team’s points in the game.

In Boston’s 92-90 triumph over Minnesota on Wednesday night, none of Boston’s second-unit players had a minus rating, with four of the five who played having a plus-2 rating or higher. Four of the five Boston starters, meanwhile, had a minus rating, and the other one, Rajon Rondo, had a rating of zero.

“[They’re] taking so much pressure off not only myself, but the other four starters,” Kevin Garnett said of Boston’s reserves. “And you need that. It refreshes your legs; you know, better bench, experienced bench — all that comes into play.”

None of the Celtics are surprised that Boston’s newcomers have fit right in.

“They’re veterans,” Rivers said. “If they were young guys we’d be behind, because you have to teach a young guy how to play the system, how to play basketball, and what their roles are, and you have to actually talk them into it. Veterans come in and pretty much accept their roles immediately, for the most part, and jump into it.”

“I knew Rasheed, and just playing against Marquis, I knew that those guys are the type of players that we needed, and they have really fit in,” Paul Pierce said. “They’re the type of glue guys. They’re not troublemakers. They don’t look for their stats. They’re unselfish. Those are the type of guys we [wanted] when we are looking for free agents, and they have really meshed well.”

Wallace is big and physical enough to defend in the post, and he is also a dangerous 3-point threat who spreads the floor and opens things up for his teammates. Seventeen of Wallace’s 23 field goals this season have come from behind the 3-point line. He has made 42.5 percent of his 3-pointers (17-for-40) while making 6 of 13 two-point shots.

“I don’t mind, if they’re good shots,” Rivers said of Wallace’s shot selection. “I’m never going to argue with a wide-open three from Paul (Pierce), Ray (Allen), Eddie (House) or Rasheed. If they’re open, they should shoot them. So I don’t mind the balance, as long as the ball starts from the inside, which it’s doing, really. Most of our threes have come off of dribble penetration or posts, and they’re double-teaming. I can live with those all day.”

Daniels, who can run the point and provides flexibility at the wing, and Wallace are typically the first two players off of the bench. Because Davis is out, Williams, who provides size and toughness, hasn’t been far behind.

Wallace is averaging 11.2 points and 4.5 rebounds, and Daniels 5.2 points and 2.8 assists. Williams is off to the best start of his career, at 7.5 points and 5.7 rebounds.

“We’ve got guys who can do a plethora of things,” House, a reserve guard, said. “We’ve got Rasheed who can post up, shoot threes, pick-and-roll, pick-and-pop, defend on the post, defend outside, block shots and rebound. That’s an All-Star.

“We’ve got Marquis, who does a bunch of different things. He can bring the ball up. He can post up. He can slash. He can shoot the mid-range shot. He can get to the paint whenever he wants to. He can pass. We have a bunch of different weapons coming in off the bench.”

Because of the three new players, Rivers said he has been installing plays slowly so that they can catch up and be on the same page as Boston’s starters, who have been playing together for two-plus seasons.

But that doesn’t mean the Celtics are behind schedule. They are 6-0 — winning games by an NBA-best margin of 18.3 points — and look better than ever.