The Sun were blown out at home last month with Parker on the floor, but it's unclear if she'll be available in Sunday's rematch.
Connecticut (11-17) trails fourth-place New York by just one game in the East but hasn't aided its playoff hopes by dropping 11 of 14. The Sun, though, did snap a four-game skid Friday with an 89-79 win over San Antonio, the second of three consecutive road games.
Chiney Ogwumike made 11 of 13 shots en route to finishing with 24 points - one shy of matching a career high - and 12 rebounds. Fellow rookie Alyssa Thomas and Alex Bentley contributed 18 points apiece.
Behind their young players, the Sun took command early by jumping out to a double-digit lead in the opening period.
"Our backs are against the wall," coach Anne Donovan said. "We're trying to get into the postseason. I was pleased at how we came out in the first quarter. It just showed the sense of urgency that we sometimes lack this season."
Donovan's team hung with Los Angeles (12-15) in the early going July 13, trailing by two after one quarter, before getting outscored 53-29 in the next two periods in a 90-64 drubbing. Chiney's sister, Nneka Ogwumike, scored a team-leading 24 points for the Sparks in the first professional matchup between the siblings and No. 1 overall draft picks.
Chiney Ogwumike had a team-best 18 points for Connecticut while Jantel Lavender had 19 and Parker scored 15 for Los Angeles. Parker has missed the past two games because a strained left knee and remained in California during a 90-69 rout to West-leading Phoenix on Tuesday.
Ogwumike had 18 points but Kristi Toliver was the only other player in double figures with 14. Los Angeles trailed by three at halftime, but couldn't recover after the Mercury's 12-0 run in the third quarter and suffered its fourth loss in six games.
"The crowd got in it and we got a little rattled," interim coach Penny Toler said. "I told them, from that moment, as a team and as players you get better, come down, slow the ball down and let's execute. We didn't execute in that stretch."
Los Angeles is 2-3 since its general manager and executive vice president took over for Carol Ross on July 21 but has a comfortable lead over Tulsa for the West's final playoff spot. The Sparks trail San Antonio by a half-game for third place.