Smith's steal, jam and free throw with 31 seconds remaining extended Atlanta's lead and the Hawks held on to beat the Denver Nuggets 108-104 on Wednesday night.
Smith had 16 points and 13 rebounds on his 27th birthday. He called his three-point play "icing on the cake."
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Brewer was called for a foul. Smith added the free throw for a 106-101 lead, giving the Hawks the ability to withstand a late 3-pointer by Andre Iguodala.
Hawks coach Larry Drew called the win "a gutsy performance" as his team bounced back from Friday's 113-111 loss to Cleveland that snapped a six-game winning streak.
"I'm just happy that we pushed through it," Drew said. "The difference was we kept pushing. We didn't break. We didn't bend."
The double-doubles by Horford and Smith helped give the Hawks a 47-40 rebounding advantage over the Nuggets, who lead the NBA in offensive rebounds and rank second in overall rebounds.
"That was one of the points of emphasis," Horford said. "Coach talked about how good they are on the glass. We took the challenge and as a team we did a good job."
Lawson led Denver with his season-high 32 points. Brewer had 19.
Denver coach George Karl said the Nuggets helped the Hawks with their 20 turnovers and poor rebounding.
"We thought fundamentally rebounding and turnovers were going to be the keys to the game," Karl said. "We just didn't do a good enough job there.
"We gave them way too many extra possessions. In the end it hurt us in a close loss."
The Hawks began the night leading the NBA with 18 turnovers forced per game.
Lawson had four turnovers, including two in the final minute.
"I feel bad for him," Karl said. "He had a great game going. He was the best player on the court for most of the night until the turnovers at the end. He just had a big-time game.
"We need some other guys to jump in and start playing well, too."
Two free throws by Danilo Gallinari with 2:34 remaining gave Denver its first lead of the final period at 98-97. Lawson's 3-pointer gave Denver a 101-99 advantage before Horford hit a tying jumper.
Following a missed jumper by Denver's Kenneth Faried, Williams made two free throws. Smith then delivered the key three-point play.
"We've just got to get better in late-game situations -- me included," Lawson said.
"Letting teams get offensive rebounds, putbacks and turnovers, that's what killed us tonight. If we could have controlled that we could have won by at least 15 points."
The Hawks had first-half success with their big lineup, with Zaza Pachulia at center and Horford shifting from center to power forward. The big lineup usually benefits Horford, who has room for more scoring opportunities away from the basket.
Pachulia also thrived with extended playing time, scoring all 11 of his points in the second quarter as the Hawks took a 55-51 halftime lead.
The Hawks' biggest lead was 73-62 at the end of a 10-0 run in the third period.
Gallinari had 16 points and JaVale McGee had 11 for Denver. Iguodala shot only 2 of 10 for five points, including the late 3-pointer, and a game-high seven turnovers.
Devin Harris had 12 points for Atlanta. Williams led the Hawks with six assists.
- The Hawks ended a four-game losing streak in the series with their first win over the Nuggets since Nov. 7, 2009.
- Hawks G Kyle Korver was away from the team and with his wife, who is expecting the couple's first child. The team recalled rookie G John Jenkins from its Bakersfield NBA Development League affiliate. Jenkins did not play.
- Lawson and Andre Miller each had seven assists.