"It seems like someone has been out for us all year long," Williams said. "So we just have to keep doing what we have to do to win."
Williams had 21 points and eight assists, and the Heat beat the Atlanta Hawks 91-83 Wednesday night for their 10th victory in 11 games.
Josh Smith scored 27 points for Atlanta, which had its five-game home winning streak snapped.
Williams had eight of Miami's last 12 points, including a 19-footer he banked in against Josh Childress that pushed the lead to 85-80 with 1:03 remaining.
"They were pressing and trapping," Williams said. "but when they decided not to double-team me, I just had to be aggressive and take the shot."
On the previous possession, Childress stole Williams' errant pass and hit two free throws that brought the Hawks within three. Atlanta has lost three of four overall.
Hawks coach Mike Woodson was irritated with his team's lapses on defense.
"You're not going to beat anybody in this league giving up 20 layups," Woodson said. "That deflates everything from a defensive standpoint, but we still hung tough."
Shaquille O'Neal, who had 12 points and three rebounds, picked up his fourth foul 16 seconds into the third quarter and didn't return until the start of the fourth. He played just 21 minutes.
"He's got to be smarter," Heat coach Pat Riley said. "Sometimes, you've just got to let something go. It's too important for him to be on the floor for us. These are good players. They're old, but we've got good players. Some nights the effort and energy isn't there totally, and you can win on savvy and talent. But going down the stretch you're going to need everything."
With O'Neal in foul trouble most of the game, the Heat used Doleac for 21 minutes, the most he has played since Jan. 30. Alonzo Mourning, Miami's backup center, missed the game with a right knee contusion.
A left knee injury sidelined O'Neal until Jan. 24. Dwyane Wade, the MVP of the NBA finals, missed his 14th straight game with a dislocated left shoulder.
Miami, which is battling Washington for first place in the Southeast Division, improved to 11-3 without Wade.
"We had some sloppy moments in the second half," Riley said, "but for the most part we always found some offense and defense to get it done."
The Heat, who have won 18 of 23, took their biggest lead at 15 on Antoine Walker's free throw late in the third.
"It's tough," said Hawks forward Marvin Williams, who finished with 16 points and 12 rebounds. "We've been hot here at home."
The Hawks fell to 0-3 against the Heat this season. Atlanta has not won a season series over Miami since 2001-02.
"We got close but we couldn't get it done," Smith said. "When Shaq got in foul trouble, we thought that would be a big factor. I thought we could attack the basket."
Jason Williams, however, took advantage of the mismatches he had whenever a slower Atlanta guard tried to stop him alone.
"I just took the shots that were open tonight," Williams said. "It is critical for us to win every game we play to try and get home-court advantage in the playoffs."
- Joe Johnson, Atlanta's leading scorer with a 25-point average, missed his eighth straight game.
- The Heat improved to 29-2 when leading after three quarters and 21-1 when shooting at least 50 percent from the field.
- Miami is now 13-22 at Philips Arena.