The Shock look to sweep their home-and-home series with the Sun on Saturday night and end their home losing streak at two games.
Sims scored a season-high 30 points on 11-of-17 shooting, and Skylar Diggins added 20 as Tulsa (7-10) pulled away for a 96-83 victory in Connecticut. The Shock couldn't hold on to an early 19-4 advantage but took command for good with an 12-3 run in the third quarter and led by 19 with four minutes left.
"She's been leading up to having a breakout night," Tulsa coach Fred Williams said of Sims, who is averaging 13.6 points. "I thought tonight she was able to turn the corner and get a rhythm in her shots. We ran some sets and we did certain things offensively for her and Skylar."
Alyssa Thomas, taken No. 4 overall and two spots behind Sims in this year's draft, also had a season high with 24 points on 8-of-10 shooting in Connecticut's fourth consecutive loss. The Sun (8-10) also got 21 points from veteran Katie Douglas, but no other player reached double figures.
Connecticut is mired in its longest skid since Aug. 16-31, when it tied a franchise record with seven consecutive defeats.
"We have to do a better job - the five starters - of coming in ready to play," said Douglas, who has 46 points in her last two games. "I don't feel like recently, we've set the tone. We've given teams confidence on our own home court. We've dug ourselves holes.
"Any time you dig yourself a hole in the WNBA, you're going to exert a lot of energy and effort to come back and we're not that good, to be honest, to be digging ourselves a hole against good teams right now."
The Sun's chances of ending their woes any time soon don't appear too promising. They're 1-6 on the road heading into the start of a three-game trip.
Connecticut could also have a difficult time holding on the fourth and final playoff spot in the Eastern Conference as well. The Sun, currently one game ahead of fifth-place Washington, are beginning a stretch in which it plays nine of 11 away from home.
Tulsa, meanwhile, will attempt to move into one of the top four spots in the West during another four-game homestand. The Shock, one-half game behind fourth-place Los Angeles, swept their four games in Tulsa from June 6-15 and play nine of their next 12 at home.
The Shock won 64-58 in last season's only visit from the Sun.