Gay finished with a game-high 24 points. Conley produced 20 points, eight assists, seven rebounds and four steals.
Marc Gasol added 19 points and 10 rebounds, and Marreese Speights netted 16 points with 12 rebounds.
The Grizzlies shot 54 percent from the field in winning there season-best third in a row.
The Bulls, playing without Derrick Rose, who has a toe injury, were led by Luol Deng's 20 points and six rebounds.
The Bulls hurt their own cause by committing 19 turnovers and making just one of 13 shots from long range.