All Jimmy Butler was looking for was a clean look.

After turning the ball over with the Bulls trailing the Boston Celtics by a point in the last minute Thursday, all Butler wanted was a shot to win the game — and at redemption.

Coach Fred Hoiberg’s strategy was simple: Get the ball to Jimmy.

Butler got the ball and bided his time as the final seconds ticked away. His jump shot floated through the air, glanced off the rim and fell short. The final horn sounded, and it appeared the Bulls had allowed another game to slip through their fingers.

But as the Celtics celebrated, officials indicated defender Marcus Smart had grazed Butler’s elbow on the shot attempt and checked the video.

Suddenly, the second chance Butler had hoped for turned into a third. After he made the two free throws with 0.9 seconds left and the Celtics’ Al Horford missed a jumper as time expired, the Bulls exhaled after surviving a 104-103 thriller at the United Center.

Afterward, Butler said he agreed with the call.

‘‘A foul’s a foul; he hit my elbow,’’ said Butler, who scored 29 points. ‘‘I don’t care what nobody says. I think I make [the shot] if he doesn’t alter it like that.”

Regardless of how it happened, the Bulls (28-29) improved to 6-1 this season against the Cleveland Cavaliers, Celtics and Toronto Raptors, whom they defeated Tuesday. Those are three of the top four teams in the Eastern Conference.

Perhaps more important, a team that has endured ups and downs, finger-pointing and infighting during the course of its first 57 games found a way to come together when it mattered most.

Despite playing their third consecutive game without Dwyane Wade (wrist, illness), the Bulls salvaged a much-needed victory heading into the All-Star break.

‘‘It’s just a great win — two good ones heading into the break,’’ Hoiberg said. ‘‘We just have to make sure we come back strong.’’

For all the drama that has taken place this season, the Bulls’ victories this week against the Raptors and Celtics provided further evidence they can compete with the NBA’s top-tier teams, even when they aren’t at full strength.

But what’s yet to be seen is how the Bulls will respond in their last 25 games of the regular season. As it stands now, they are in seventh place in the East.

For as many big victories as the Bulls have earned thus far, they will have to address and overcome the inconsistency that has kept them hovering around the .500 mark all season.

The last-second victory against the Celtics — controversial or otherwise — was a step in the right direction. But Butler acknowledged it wasn’t the last one the Bulls must take.

‘‘It’s big; all wins are,’’ Butler said. ‘‘But we can’t be satisfied. We can’t settle right now. We’ve got to start winning these games, get over .500 and keep looking forward.’’

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