The Hawks have won two straight, three of four and six of nine. Memphis, the NBA's fifth-most accurate team on 3-pointers, lost its fourth straight after shooting a season-worst 1-for-15 beyond the arc.
After hitting a runner midway through the third, Smith followed with a three-point play to stretch Atlanta's lead to 52-33. He finished 11-for-19 from the field and grabbed seven rebounds.
Smith, a third-year veteran who's only 22, praised Woodson's new halftime approach. In a one-point victory over struggling Minnesota on Thursday, the Hawks scored just eight points in the third quarter.
They had 29 against Memphis.
"It got our bodies moving," Smith said. "I was happy we were able to create spurts like we did in the third quarter."
Horford has 10 or more rebounds in five straight games. The former Florida standout, drafted No. 3 overall after helping the Gators win two straight national titles, leads all rookies and ranks 11th overall with an 8.1 average.
Memphis coach Marc Iavaroni knew his team would be tired after losing in overtime the previous night in New Orleans.
"We were running on fumes all night, but I think the guys battled back pretty well," Iavaroni said. "It was real evident we didn't have any legs by the way we were shooting the ball tonight."
Down by 16 points after Horford's turnaround 10-footer late in the first, the Grizzlies went on a 16-6 run, ending with Gay's putback, to pull to 30-26.
Memphis, which dropped to 2-9 on the road and 6-14 overall, never threatened in the second half after Mike Miller's 3-pointer cut the lead to 43-33 early in the third.
"We have to be aggressive and figure out a way to score and produce even when we are having a bad shooting night," Grizzlies center Pau Gasol said. "The Hawks were basically running out on us and getting easy baskets." Had we shot the ball better, we would have probably had a chance to win."
Woodson, now 78-187 in his fourth year with Atlanta, will now preach the importance of maintaining a winning record. At 9-10, the Hawks visit Orlando on Monday.
"I've been saying all year that if we can play .500, we'll be in position to make the playoffs," he said. "It's a long season. We just have to stay the course."
The Hawks' average age is 25 years, 193 days. Chicago, which is second in the NBA, is an average of 77 days older. ... Atlanta G Josh Childress was out with a strained groin, but he hopes to return against the Magic. .. Grizzlies G Damon Stoudamire started but was scoreless while shooting 0-for-6 from the field after missing the Hornets game. ... The Hawks are 6-5 at home. ... Woodson estimates that G Tyronn Lue could miss the next two weeks with a strained left calf.