Lyttle added 10 rebounds and made a pair of 3-pointers during a key stretch early in the fourth quarter and then nine points in the two extra periods as the Dream won their fourth game in the past five.
DeWanna Bonner had 27 points, 15 rebounds and six steals to lead the Mercury (4-12), who have played since a May 31 loss at Atlanta without injured star Diana Taurasi. Phoenix has lost five of six and is 3-10 without Taurasi. Taurasi remains sidelined by a strained left hip flexor.
The Dream (8-8) used a 16-0 run to end the third period and an 8-3 start in the fourth quarter to erase a 17-point deficit and led by five with 1:03 left in regulation.
The Dream did not play Angel McCoughtry, the league’s leading scorer at 22.6 points per game and a member of the U.S. Olympic team with a week before the WNBA breaks for London.
Atlanta led 75-70 with 1:03 left on Lyttle’s jumper but Charde Houston scored in the lane and then Bonner hit a 23-footer to tie it with 15 seconds remaining after Phoenix forced a Dream turnover on the other end, leading to the first extra period.
The teams traded baskets for much of the first overtime and both teams missed shots in the final six seconds to force a second overtime.
Tiffany Hayes added 23 points, six rebounds and four assists for Atlanta, which was outrebounded 63-39 but made 25 of 49 from the field after halftime following a 32.5 percent performance in the first half.
Phoenix scored the first six points of the second half and then ran off a 13-2 spurt to take a 56-39 lead with 3:23 left in the third quarter. However, Catherine Kraayeveld hit back-to-back 3-pointers in a 16-0 run by Atlanta to end the period, leaving the Dream down 56-55 going into the final quarter.
Candice Dupree, the team’s second-leading scorer through the first nine games, played for the first time since June 17, scoring six points in nine minutes.