Sparks rookie Nneka Ogwumike added 22 points, 13 in the second half, for the Sparks, who have won three of their first four games of the season.
Candice Dupree had 24 points to lead the Mercury (1-2).
Parker had eight of her points in the final five minutes after Phoenix rallied to within 83-80 after Los Angeles had opened up an 11-point lead late in the third.
Kristi Tolliver, who added 18 points for the Sparks, started a key stretch for the Sparks with a pair of free throws with 5:43 left and Los Angeles up by three. DeLisha Milton-Jones found Parker all alone underneath the basket for an easy basket and Los Angeles led 87-80. Phoenix never got closer than five.
Tolliver also scored five points in the final 90 seconds of the third quarter as Los Angeles led 73-64 going into the final period.
Until the late third quarter stretch, neither team led by more than seven.
Parker scored 14 points and had six rebounds and three blocked shots to help the Sparks take a 43-37 lead at the break.