Glory Johnson added 18 points and six rebounds as the Shock (7-23) snapped a four-game losing streak.
Lynetta Kizer had 19 points and seven rebounds for Phoenix (7-23), which has lost four of its past five.
Tulsa took advantage of 21 Phoenix turnovers, converting them into 25 points, seven in the final period.
The Shock ran off seven straight points midway through the fourth quarter to take an 87-78 lead with 3:20 left.
With three starters out because of injury, Phoenix used just seven players on Friday, including three rookies.
Olympian Diana Taurasi, who has missed 22 games this season, much of it with a hip flexor, sat out for the second straight night. The league’s second-leading scorer, DeWanna Bonner, also did not play because of a sore back.
Riquna Williams added 16 points, six rebounds and four assists for Tulsa, which has beaten Phoenix only twice in the past 12 meetings.
Free agent and Phoenix native Dymond Simon, in just her sixth pro game, had 16 points, six assists, six rebounds and three steals for the Mercury.
Roneeka Hodges hit a pair of 3-pointers and the Mercury missed 13 of their first 18 shots as Tulsa opened up a 22-13 lead after one period. Phoenix scored the first seven points of the second quarter and made 14 of 22 from the field in the period and tied it at 42 at the break.
The teams traded baskets much of the third quarter although Alexis Hornbuckle’s 3-pointer from the top of the key gave Phoenix a 68-63 lead in the final minute of the quarter. However, Latta hit a 3-pointer for Tulsa to put the Shock within two going into the final period.