Popovich will face his former assistant for the first time Monday night when the Spurs visit the 76ers in search of a fifth straight victory.
Philadelphia (4-3) took a long time to decide on Doug Collins' successor before opting Aug. 14 to hire Brown, who played for Rick Pitino at Boston University.
The 52-year-old Brown's association with Popovich is more notable since he was part of three NBA title teams with San Antonio as an assistant and won another with the Spurs when he served in the basketball operations department in 1998-99. He left briefly to coach in Australia before rejoining the Spurs in 2002 as the team's assistant coach/director of player development and later moved to the bench under Popovich in 2006.
These coaches had different outlooks after their clubs' most recent games, with Brown happy after a defeat and Popovich not entirely pleased despite an easy victory.
Philadelphia fell 127-125 in double overtime Saturday at Cleveland after posting a 94-79 home win over the Cavaliers the night before.
"That was a great NBA game," Brown said. "The only negative is that we lost. I told our guys how proud I am of them because they continued to fight and find any way possible to win."
The demanding Popovich watched his team lead by as many as 37 points in Sunday's 120-89 rout at New York. It marked the Spurs' first double-digit victory and he said before the game that his team was playing C+ or B- basketball.
A rout in which no player was forced to log 26 minutes improved his mood, although the coach feels his veteran team can still play better.
"I thought tonight we played a good, solid B+, A- game," Popovich said. "There were some good things out there."
Danny Green scored 24 points and added a career-high 10 rebounds and Tony Parker scored 17 as San Antonio (6-1) opened on a 21-4 run, built an 18-point lead after one quarter and was never threatened. The Spurs shot a season-high 53.9 percent.
"We just played our game and we made shots," Parker said. "When you make shots it helps, and the ball movement was great."
Now San Antonio will try to slow down one of the league's highest scoring teams in Philadelphia, averaging 105.9 points. Evan Turner is off to a strong start in averaging 23.4 points while Michael Carter-Williams leads all rookies in scoring with 18.4 points per game.
Sixers guard James Anderson will face his former team for the first team. Anderson, a first-round Spurs pick in 2010, has started his first seven games with Philadelphia after coming over as a free agent after Houston waived him.
Tim Duncan averaged 20.0 points and 12.5 rebounds as San Antonio swept two meetings with Philadelphia last season to extend its win streak in the series to four. Spencer Hawes averaged 19.0 points to lead the Sixers in the two defeats.