Tom Thibodeau and the Knicks officially are headed back to the playoffs for the second time in three years following last year’s step-back campaign, stamping the publicly stated goal of team owner James Dolan from January.

The Knicks won their second consecutive game with injured All-Star forward Julius Randle out of the lineup on Sunday night, dispatching the injury-riddled Wizards, 118-109, at the Garden to clinch no worse than the No. 6 postseason seed in the Eastern Conference.

“I said it at the time — I love that the owner has great belief in the team — that’s what I want,” Thibodeau said after the game. “Our job is to put the work in each day. But there’s no trick to this, there’s no magic to this, there’s no shortcut to it.

“It’s a great accomplishment because it’s one of the goals, one of several. It’s the next step along the way. So, keep going, and that’s where the focus is. We know how important the next game is. So get ready for Indiana. But just keep checking the boxes as we go.”

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Jalen Brunson followed up his career-best 48-point effort in Friday’s win in Cleveland with 27 points and eight assists, while Quentin Grimes drained six 3-pointers and also finished with 27 points as the Knicks (46-33) won their fourth straight game overall to avoid any potential of appearing in the 7-10 play-in tournament.

They also inched ever-closer to securing a 4-5 matchup in the first round against Donovan Mitchell and the Cavaliers, maintaining a 2 ½-game lead over the Nets with three to play beginning Wednesday night at Indiana.

“It’s a great feeling. It’s something you strive for,” Brunson said. “You want a chance to compete. The fact that we get further on in our season is great. But we’ve still got a lot of work to do.

“I think first and foremost we want to finish the season as strong as we can. Even getting in the playoffs we don’t want to coast. We want to continue to get better, continue to find ways to make each other better and make sure we’re staying focused as we’re going forward. That’s what’s most important.”

With Randle on the bench wearing a boot to protect his sprained left ankle, and RJ Barrett also sidelined with a non-COVID illness, the Knicks’ improved depth shone through again, with fill-in starters Immanuel Quickley and Obi Toppin netting 22 and a season-high 21 points, respectively.

According to MSG, it marked the first time the Knicks have had four players with at least 20 points apiece since 2018.

“It’s great. We have a lot of hard-working guys on this team,” Brunson said. “Whenever their number is called, they’re always ready, they’re always prepared. … A lot of guys played well tonight, stepped up. We’ve got a lot of room to grow.”

Corey Kispert scored 29 points to lead the depleted Wizards, who were without four starters, including three-time All-Star guard Bradley Beal and former Knicks forward Kristaps Porzingis.

Popular former Knicks big man Taj Gibson (14 points) sank consecutive long-range buckets early in the second quarter as the Wizards went ahead, and Kispert rattled home his third triple of the half and 20 points as the Wizards led 61-53 at intermission.

The Knicks recaptured the lead on Quickley’s transition dunk and Brunson’s two free throws just past the midway point of the third, before Grimes’ third 3-pointer of the game and Brunson’s weaving bucket made it a 74-69 game en route to a seven-point advantage entering the final period.

Consecutive buckets from beyond the arc by Toppin and Quickley extended the lead to 11 early in the fourth, and Grimes’ sixth 3-pointer of the night made it a 110-94 game with 4:01 remaining to seal the Knicks’ coveted playoff berth.

“That’s the goal to get into the playoffs and now the goal is to be the best team we can be at the right time,” midseason acquisition Josh Hart said. “We got Indy next, so just got to go out there and continue to grow, continue to improve, and play our best basketball at the end of the day.

“It’s a good accomplishment, it checks that box, but we gotta continue to get better.”