Harden, who signed a five-year, $80 million contract extension with Houston following the trade, had 37 points, 12 assists and six rebounds in a 105-96 win at Detroit in his debut on Wednesday night.
Houston led after each of the first three periods. The Rockets took a 68-52 lead in the third before Atlanta cut the deficit to 81-74 at the end of the quarter.
A basket by Smith with 7:12 remaining gave Atlanta an 88-87 lead, its first since the opening period.
"We were just trying to put together as many stops as we could," Williams said. "We battled our way back into the game to even get it to that point."
The Rockets are 2-0, but McHale said the team needs work on closing out wins.
"We need a few days together in the gym where we can slow some things down and figure out how we want to finish games," McHale said.
After a preseason of sampling lineup combinations, Drew had two newcomers — Devin Harris and Kyle Korver — join Al Horford, Smith and Jeff Teague. Drew said he had "a little indecision" about Harris starting at shooting guard as the coach worried about the defensive matchup with Harden, who at 6-foot-5 is at least 3 inches taller than Harris.
DeShawn Stevenson, who could match Harden's height — and at least come close to matching Harden's beard — became an important player off the bench for Atlanta.
Stevenson had 12 points on four 3-pointers, including one at the buzzer to end the first half.
Teague had 14 points and seven assists and Horford had 14 points.
The Rockets had a 58-36 advantage in rebounds.
"We have some things that we really have to focus in and work on," Drew said. "There were areas in this game where we weren't very good, very polished, particularly on the boards."
Drew said his perimeter players were beaten for too many long rebounds.
"We didn't play well, yet we gave ourselves a chance in fighting back," he said.
Notes: Houston F Patrick Patterson started after missing the opener with a strained left quad. C Greg Smith (strained left foot) did not play. ... Harden's previous career high was 40 points against the Suns on April 18. ... Hawks C Johan Petro was inactive. ... Stevenson fouled out in the final minute. ... Harden is the first player to score 40 points against Atlanta since LeBron James had 43 points on March 18, 2011.