The Bobcats made a bid for what would have been their eighth win of the season, but they were outscored 28-15 in the final period. Charlotte has lost a franchise-record 19 games in a row.
Conley's free throws made it a two-possession game and wrapped up a 20-point performance. Zach Randolph added 14 points for the Grizzlies, winners of three in a row.
Memphis climbed to within one game of the Los Angeles Clippers for fourth place in the Western Conference and the home-court advantage that goes with it in the opening round of the playoffs.
Gerald Henderson produced a career best with 32 points for Charlotte.
2014: The Year in Music [PHOTOS]