The Dream look to avoid their seventh loss in eight regular-season meetings in Connecticut on Sunday when they try to send the Sun to their second three-game losing streak in seven games this season.
After totaling 19 points and going 5 of 12 in her first four games, Hayes gave Atlanta (3-2) a boost Friday by scoring 20 on 6-of-9 shooting in an 80-69 home win over Seattle.
The third-year guard, who came within three points of matching a career high, had been held scoreless on just two field-goal attempts in an 82-77 loss to Indiana last Sunday.
"The first shot went down, the confidence goes up," said Hayes, who averaged 11.3 points in 2013 but had been in double figures in only one of the first four games this season. "It's always just whatever the team needs from me."
Sancho Lyttle and Erika de Souza also played well with a combined 27 points and 18 rebounds to help the Dream end a two-game losing streak following a 2-0 start.
Now Atlanta hopes the supporting cast can continue easing the pressure on high-scoring star McCoughtry, who finished with 18 points and a season-high eight assists Friday.
The two-time WNBA scoring leader is averaging 21.3 points, 5.5 assists, 5.0 rebounds and 2.8 steals, though she missed an 87-73 loss May 24 at Chicago with a shoulder injury.
McCoughtry scored 28.4 per game to help the Dream take three of five from the Sun in 2013. Though Connecticut finished with the league's worst record, three of those five meetings were decided by two points or less.
Atlanta dropped two of the three road matchups, falling to 1-6 in Connecticut during the regular season since 2011. The Dream, however, might be able to break through this time against the Eastern Conference-worst Sun.
After it had just two wins through seven games en route to a franchise-worst 10-24 record last season, Connecticut has gotten off to a 1-6 start in 2014 following Friday's 101-82 loss at Chicago.
Kelsey Bone finished with a team-high 20 points and Chiney Ogwumike had a double-double with 11 points and 10 rebounds. The rookie forward has certainly been a bright spot, averaging 17.2 points and 9.2 boards.
The Sun are 0-4 on the road, but have split their two home games. Ogwumike - the No. 1 pick in this year's draft - had 18 points in a 71-59 win over Seattle on May 23.
Connecticut, one of the WNBA's worst shooting teams at 39.0 percent, will try to bounce back after missing 15 of 19 shots in the second quarter Friday. Defensively, the Sun gave up their most points since a 107-101 loss - also at Chicago - in June 2011.
That doesn't bode well heading into a matchup with an up-tempo Atlanta team that ranks among the league leaders with a 46.8 field-goal percentage.