Nevarez completed two conventional three-point plays on tough layups in transition following steals, and added two more baskets on a jumper from the right wing and another steal and layup to give the Gaels a 27-20 lead with 4:06 left in the third quarter.
The Saints -- who had won three of their previous four games -- closed to 29-28 late in the third quarter before Costello started going to work. She capped the third period with a basket inside, then scored the first three baskets of the fourth quarter, taking advantage of open space on the baseline.
Costello finished with game-highs of 15 points and 12 rebounds for the Gaels, who took a 39-28 lead on Nevarez's final basket with 4:57 left in the fourth.
St. James was not done. Hilary Shoop scored inside with 4:12 left before Caroline Salisbury made three straight baskets, including the game's only 3-pointer, to cut the lead to 39-37 with 2 minutes to play. Salisbury finished with 13 points and four steals for St. James.
"They've been playing great the last two weeks," Saints coach Joanna Ruderman said. "I wish they had played like this all season. They've really come together with their passing and defense. They're giving it their all, especially the seniors."
"We got up and relaxed, and Salisbury made a few baskets," Rideout said. "It was a typical girls game between Goretti and St. James. We got the lead, they didn't give up and kept fighting until the end."
But the Saints could not find the net again, and Costello's final basket with 1:13 left and two foul shots by Dominique Forsman with 2.1 seconds to play sealed the win.
Maggie Garvey had eight points, seven steals and three assists to aid Goretti's cause.
Courtney Peterson had eight points, nine rebounds and five steals for St. James. Wills had 10 points, seven rebounds, five assists and four steals, and Taylor Deveaux added eight rebounds.
Goretti 43, St. James 37
ST. JAMES (6-14)
Wills 10, Morrow 2, Salisbury 13, Worth 4, Peterson 8, Deveaux 2. Totals 16 4-5 37.
ST. MARIA GORETTI (13-15)
Costello 15, Garvey 8, Shoop 2, Nevarez 12, Forsman 2, Harrell 2, Rzomp 2. Totals 18 7-14 43.
St. James 9 9 10 9 -- 37
Goretti 12 5 14 12 -- 43
3-point goals -- St. James 1 (Salisbury). JV -- Goretti, 39-20 (G: Forsman 25; SJ: Berry 6).