Joe Smith added a season-high 18 points and had 12 rebounds, and Andre Miller had 11 points and 12 assists for Philadelphia.
"We got it. That's what we've been working toward," coach Maurice Cheeks said. "We talked about consistency for so long. Now we have to build off that."
In a matchup of teams vying for more pingpong balls in the draft lottery, the Grizzlies improved their chances.
Pau Gasol had 31 points and 13 rebounds and Mike Miller scored 27 for Memphis, which has the worst record in the NBA (15-45) after making the playoffs three straight years.
The Sixers (21-38) are third-worst ahead of Boston. The team that finishes last isn't guaranteed the first pick in June's draft. However, that team will have the best chance to win the lottery.
"I'm proud of the effort, but you have to do the little things to win in this league and tonight we didn't do the little things," Grizzlies coach Tony Barone said.
Coming off an impressive victory over Phoenix that prevented the Suns from becoming the first team in league history to sweep its road games against the opposite conference, the Sixers almost reverted back to their losing ways.
They committed 12 turnovers and trailed by three at halftime, despite shooting nearly 60 percent.
The Grizzlies went on a 9-2 run to start the fourth quarter, but Korver ended it with a 3-pointer and the teams stayed close the rest of the way.
Iguodala's driving layup put the Sixers ahead 103-100 in the final minute of regulation, but Mike Miller nailed a 3-pointer from the top of the arc to tie it with 4.9 seconds left. Iguodala's fallaway shot missed as the buzzer sounded, sending it to overtime.
Korver scored the first points in the extra session on a baseline jumper and made a pair of free throws to give the Sixers a 107-105 lead. Andre Miller followed with a steal and layup to extend the lead to 109-105, and Smith's jumper iced it.
After starting the season 3-0, the Sixers lost 19 of their next 21. They're hoping to continue their improved performance and finish the season off on a strong note.
"We have a long way to go," Korver said. To win three games in a row in the NBA, that's great when you haven't done it in a while. But, it's really not a big deal."
On a night when young fans received Andre Miller replica jerseys, the point guard dazzled with several nifty passes. Miller found Samuel Dalembert for an alley-oop pass on an inbounds from behind the basket as the Sixers took their biggest lead to that point, 34-28, in the second quarter.
"He's a pleasure to play with," Korver said of Miller, acquired in the trade that sent Iverson to Denver.
Said Cheeks: "He orchestrates the whole thing."
The Grizzlies outscored Philadelphia 20-11 after Dalembert's dunk and took a 48-45 lead at halftime.
"We're just not playing well," Mike Miller said. "We're finding ways to lose games instead of ways to win them and that's disappointing. We have to keep plugging away and try to win games."
Sixers rookie F Rodney Carney sat out his second straight game with a torn rotator cuff and labrum in his right shoulder. ... The Sixers are 16-26 since Iverson played his last game with Philadelphia. ... Memphis G Chucky Atkins didn't play because of a sprained right ankle. ... The teams split the season series.