Thad Young had 14 points and 16 rebounds and Royal Ivey chipped in with 17 points for the Sixers, who are 5½ games behind Milwaukee for the final playoff spot in the Eastern Conference with 25 games left.
Stephen Curry scored 30 and Klay Thompson added 29 for the Warriors, who've lost four in a row.
Despite losing 10 of 13, Golden State remains sixth in the West. The Warriors are one game up on eighth-place Houston and 3½ ahead of the Los Angeles Lakers, who are fighting for the last spot.
The Sixers overcame deficits of 16 in the first half and 11 in the third quarter and took an 82-81 lead into the fourth.
The teams went back-and-forth until Young's layup put Philadelphia up 96-94 with 3:15 left. Turner followed consecutive misses by the Warriors with a jumper from the corner. He nailed another one for a 100-94 lead.
But Thompson answered with a 3-pointer. After two failed possessions, Holiday hit a jumper to give the Sixers a 102-97 cushion and ice it.
Holiday and Turner combined for 18 of Philadelphia's 22 points in the final quarter.
Sixers coach Doug Collins ripped his team's effort following a home loss to Orlando earlier in the week. They played better in a loss at Chicago the next time out and followed up with their best performance in weeks against the Warriors.
Thompson came out firing in the third quarter, scoring 12 straight points for the Warriors to turn a three-point lead into a 66-56 margin. Thompson started off with two mid-range jumpers, then nailed two 3-pointers and finished with a long jumper that was later changed to a 3.
A 3-pointer by Ivey - his fourth without a miss - got the Sixers within 66-61. Consecutive layups by Turner capped a 6-0 run and momentarily gave Philadelphia its first lead, 73-72. Then a review of Thompson's jumper from a few minutes earlier was ruled a 3-pointer so the score went back to a tie.
The Sixers then went up for real, 77-75, on Arnett Moultrie's alley-oop slam off Turner's pass.
The injury-plagued Sixers played without guard Nick Young, who was sidelined by a left ankle sprain. They haven't had center Andrew Bynum all season and lost guard Jason Richardson for the year last month.
Down 49-33 in the second quarter, the Sixers climbed back in it with an 11-0 run featuring three straight 3-pointers by Turner, Holiday and Wright. Turner's 3 was his first in more than a month, snapping an 0-for-14 slump from beyond the arc.
He hit another a few minutes later, helping the Sixers close out the first half on an 18-5 run to get within 54-41 going into the third quarter.
Curry, who scored 54 in a loss to the Knicks at Madison Square Garden on Wednesday night, appeared on pace for another big night early. He had 13 in the first quarter to help Golden State build a 13-point lead. The Sixers forced him away from the arc, so he got four of his first five baskets on driving layups.
Thompson took five 3-pointers in the first quarter, missing four.