Camille Little added 15 and Shekinna Stricklen had 15 points and 11 rebounds for the Storm (9-10), who beat the Mercury for the second time in six days.
DeWanna Bonner scored 18 points, Lynetta Kizer had 14 and Alexis Hornbuckle added 13 for Phoenix (4-15), which matched a franchise record with six third-quarter points, set twice previously and most recently in 2008.
The Mercury have lost six straight and eight of their past nine.
The game was the last for both teams before the league's monthlong break for the Olympics.
Smith connected on all five of her field-goal attempts, including three 3-pointers, as the Storm ran out to an early 27-20 lead.
Phoenix rallied late in the second after point guard Samantha Prahalis left the game with a left ankle injury, pulling within 39-37 on a 3-pointer by Bonner with 1:17 to go.
Seattle pushed the lead back to 41-37 at the half and held Phoenix without a field goal over a 7:54 span of the third and fourth quarters.
Prahalis returned at the start of the second half and played the entire second half, scoring the last of Phoenix's third-quarter points on a free throw following a technical foul.