Iguodala had the ball at the top of the arc, drove to his left and made a left-handed toss over the outstretched arm of Marc Gasol for an 89-87 lead.
Hakim Warrick, who scored a season-high 31 points for the Grizzlies, missed a dunk and Iguodala and Samuel Dalembert sealed the win from the free throw line.
Andre Miller had 24 points and Thaddeus Young scored 12 for the Sixers, who finished 5-2 on their season-long homestand.
Philadelphia (27-24) is three games over .500 for the first time since winning the first three games of the 2006-07 season, and enters the All-Star break with a 14-4 mark since Jan. 6.
Mayo finished with 16 points and Mike Conley had 13 for the Grizzlies.
Sixers coach Tony DiLeo told Iguodala to enjoy this All-Star break because he predicted this would be the last one off for a few years with the way the guard has blossomed into their best player. He shook off a slow start and scored eight straight points in a 2-minute stretch late in the fourth period to help Philadelphia hold off the pesky Grizzlies.
He tied the game at 82 with 2:10 left, then came down a couple of possessions later to swish an 18-footer for an 84-82 lead.
Iguodala sank two free throws with 1:10 left for an 86-84 lead. The Sixers have won 14 of 18 games to enter the break as one of the hottest teams in the NBA. They almost let this one slip away.
Warrick led the charge back from a 12-point hole and his layup late in the third period tied the score at 57. Iguodala converted a three-point play and Miller hit a pair of jumpers to give the Sixers a 64-59 lead at the end of the quarter.
Miller was nearly flawless from the floor and scored 16 points in the first half to help the Sixers lead 41-37 at halftime. But he had only one assist and none of the other Sixers got involved in the offense. Iguodala, their leading scorer at 17.8 points, had only one basket in the half and that was on a dunk with 54 seconds left in the second period.
Notes: The Sixers are 18-10 under DiLeo. ... Memphis held a 43-26 edge on the boards. ... Miller had nine assists.
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