Miami’s Kasib Powell, left, fouls Boston’s Leon Powe in the second quarter of last night’s blowout victory at the TD Banknorth Garden.

AP / Michael Dwyer

BOSTON — Boston sent a message to the rest of the teams on its schedule last night.

The Celtics are not going to take it easy on them just because they have a losing record or because Boston is poised to lock up home-court advantage throughout the playoffs in the near future.

Facing lowly Miami last night at the TD Banknorth Garden in front of a crowd of 18,624, the Celtics crushed the Heat (13-60) — the worst team in the NBA — 88-62 in a game that Boston dominated from start to finish.

“We are supposed to do that [to Miami],” Boston captain Paul Pierce said of the blowout. “They have D-Leaguers out there, so I think we just handled our business. They put about four or five guys from the D-League in and we did our business. We are supposed to do that. We knew this was a game that we were supposed to win and we just focused from the jump and went out and did it.”

The win moved Boston (58-15) one game closer to securing home-court advantage throughout the playoffs. New Orleans (50-22) has the second-best record in the NBA, but the Celtics hold a firm lead over the Hornets for the top overall seed.

Last night’s win was Boston’s third straight victory by 20 points or more and it gave the Celtics their first season sweep of Miami in nine years.

Boston held Miami to an NBA-record for fewest field goals allowed in a game in the shot-clock era — 17. The previous record was held by Chicago, which made only 18 field goals against Miami on April 10, 1999.

“Any time you can become part of NBA history is something special,” Boston guard Ray Allen said. “I think for the most part we did it as a team.”

The Celtics out-rebounded Miami, 54-31, and limited the Heat to just 28.8-percent shooting from the floor (17-for-59).

“[Boston] is one of the best defensive teams in the league,” Miami guard Ricky Davis said.

“Our defense has been our bread-and-butter all year and tonight was no different from that,” Boston forward Kevin Garnett said.

“We can still get better,” Pierce said.

That’s a scary thought for other teams.

“We need to do a better job against the Philadelphias and everybody else,” Pierce said. “I mean, there aren’t too many teams we are going to play that are over .500, but it doesn’t matter. We want to go into the playoffs playing well.”

The Celtics used last night’s game to work on getting their plays down pat and to get players such as Tony Allen (19 minutes), Sam Cassell (18:29) and PJ Brown (11:24) more playing time to prepare for the playoffs. The starters were rested in the fourth quarter after Boston had built a 68-48 lead through three periods.

“I use the term sharpening tools, and that’s basically what we are doing,” coach Doc Rivers said. “We feel like we just have to keep sharpening it every day. We’ve talked about it for at least the last month or two that the opponent is us every night and no one else, and that’s how we have to face these next games.”

Boston has only one team left on its schedule that has a winning record, Washington, but if Boston’s last three games are an indication of things to come, the Celtics are going to keep playing inspired basketball the rest of the way.

“Our motivation is going to continue to be to go out there and get better and try to win home court right now regardless of who we are playing,” Pierce said. “We can’t have any letups right now.”

They certainly didn’t have a letdown last night. Boston rocketed out to a 32-13 lead after one quarter of play and never let up.

Leon Powe led the way with 17 points and 13 rebounds. Garnett (12 points, 8 rebounds), Allen (10 points, 5 rebounds), Pierce (10 points, 4 assists) and Cassell (9 points) also played well.

Davis (6 rebounds) and Chris Quinn (8 assists) each had 14 points for Miami.

roblee@projo.com