Chicago (17-5) had a chance to win at Miami on Sunday, but Rose missed two free throws and then a potential tying jumper with 3.7 seconds left as the Bulls fell 97-93.
Rose -- who had made his previous 29 fourth-quarter free-throw attempts -- did tied his season high with his second straight 34-point performance, but was more concerned with the points he didn't score.
"This is so surreal right now knowing that I had a chance to win the game," said Rose, who also had 34 points in Friday's 107-100 win over Milwaukee. "And this time it didn't work out.
"I let my team down."
The reigning league MVP now looks to help the Bulls avoid their first back-to-back regular-season losses since Feb. 5 and 7. Fortunately, they've won their last six meetings with the Wizards -- the last three by an average margin of more than 20 points.
Rose sat out with a sprained toe when these teams met Jan. 11 in Chicago, but John Lucas III picked up the slack by scoring 25 points in the Bulls' 78-64 victory. The 64 points scored by the Wizards in that contest were a franchise low.
Luol Deng, who had 12 points and 15 rebounds for the Bulls in the Jan. 11 win, will miss Monday's rematch with torn ligaments in his left wrist.
This time, Chicago is likely to rely heavily on a healthy Rose, who is averaging 25.1 points in his last seven games against the Wizards (4-16) -- winners of two of three under interim coach Randy Wittman to match their victory total in 17 games under the now-fired Flip Saunders.
JaVale McGee scored 22 points and 10 rebounds in Saturday's 102-99 victory over Charlotte, which Washington also beat 92-75 on Wednesday in Wittman's debut.
"We had good balance," Wall said. "I think (Saturday) nobody cared about who scored. We just went out there and played basketball. That's what you've got to do to win. Some nights it's going to be different people leading in scoring and you've just got to live with it."
The Wizards will need a similar effort Monday if they are to end their six-game skid against the Bulls, whom they haven't defeated since a 101-95 home win Feb. 22, 2010.
Wall went 3 for 14 from the field and scored only nine points in the most recent meeting at Verizon Center, as Rose scored 21 to lead Chicago to a 105-77 win last Feb. 28.
Wall is averaging 13.3 points and 4.3 turnovers in four career games against Chicago.