De Souza had 23 points and 11 rebounds, and Schimmel scored all seven of her points in the fourth quarter and tied the franchise record with 11 assists in Atlanta's 79-75 victory Friday night in the season opener.
''This is the year that we can go farther,'' de Souza said after Atlanta outscored San Antonio 48-36 in the paint. ''Cooper is always asking everybody to play inside; this helps me a lot. This is going to be the year for us.''
The Dream led 38-36 at halftime and made it 52-43 on McCoughtry's free throws with 4:21 to go in the third period. San Antonio closed the quarter with a 13-3 run, taking a 56-55 lead on Danielle Robinson's drive with a second to go in the period.
Robinson scored 17 of her 23 points, but made just one of two free throws with 57 seconds left to leave it tied at 73.
Then, after McCoughtry wiggled free for a go-ahead layup with 42 seconds left, Robinson was called for a charge when she appeared to score on a tying drive with 39 seconds left.
Schimmel rushed a shot moments later, but quickly atoned for it with a steal after San Antonio's Kayla McBride dribbled the ball off her foot. That led to a pair of free throws by the rookie with 6.4 seconds for a 77-73 lead.
Schimmel missed her only shot attempt through the first three quarters yet added eight assists in that time. She hit two of five shots in the final period, including a 3-pointer that tied it at 62 with 8:02 remaining.
Given the outcome, Cooper was OK with Schimmel's ill-advised jumper 16 seconds earlier when there was still about 10 seconds on the shot clock.
''I'm giving her a little leeway,'' said Cooper, who led the Los Angeles Sparks to WNBA titles in 2001 and '02. ''You don't stop a great player like that because you just let her make it happen. Now, had we lost, I'd probably be saying something different.''
The Stars took a 72-68 lead on two McBride free throws with 3:10 left in the game, but suffered three turnovers and missed three of four free throws the rest of the way. San Antonio reserve forward Danielle Adams hit a short jumper for the last of her 18 points with 3 seconds left.