Rose, who had missed three games with a foot/ankle injury contributed 11 points and eight assists as the Bulls took a two-and-a-half game lead over the Heat with two games left in their schedule.
A win by the Bulls in either of their games or a loss by Miami, who have three games remaining, would give the top seed to Chicago.
"We're not worried about no other team," Rose said. "We're just trying to win every game."
The Heat were surprised 86-84 by the Washington Wizards on a last-second field goal.
In Chicago, Loul Deng scored 22 points and Richard Hamilton 19 for the Bulls, who held defending champion Dallas to just eight points in the first quarter.
"They are a tough team to put the ball in the basket against," Dallas coach Rick Carlisle said of the Bulls' first quarter defense.
Dirk Nowitzki scored 17 points for Dallas. Rodrigue Beaubois added 16 as he started for Jason Kidd, who along with Jason Terry sat out the game to rest as the Texan side prepare for the playoffs.
Elsewhere, the Denver Nuggets clinched a Western Conference playoff spot with a 118-107 road victory over the Phoenix Suns.
Ty Lawson sparked the Nuggets with 29 points, making all five three-point attempts, and 10 assists.
Shannon Brown topped Phoenix with 28 points and Steve Nash collected 13 assists to pass Oscar Robertson for fifth place on the NBA all-time list.
For the Suns to make the postseason, they must win at Utah on Tuesday and defeat the San Antonio Spurs on Wednesday.
Philadelphia's playoff hopes got a big boost with a 109-106 overtime win over the playoff bound Indiana Pacers.
One more win would clinch a postseason spot in the East for the 76ers, who snapped a seven-game Indiana winning streak.