Zach Randolph had 23 points and 10 rebounds for Memphis, which has won a season-best six straight and 11 of 12 overall. Marc Gasol had 19 points and James Johnson scored 14.
Brandon Knight led Milwaukee with 23 points, including 18 in the second half. He also had seven assists and six rebounds.
Ersan Ilyasova finished with 14 points and 13 rebounds for the Bucks, who have lost six in a row. Khris Middleton scored 12 points, while Larry Sanders and Caron Butler finished with 10 each.
The Grizzlies were playing their first game without Conley, the starting point guard who sprained his ankle in Friday night's win at Minnesota. The team announced before the game that Conley will miss at least a week.
Memphis outscored the Bucks 56-41 in the second half. Calathes not only set career highs for points and minutes (40), he shot 8 of 12 in the game and 4 for 5 from 3-point range without committing a turnover. His previous high was 11 points against Houston on Jan. 25.
Memphis struggled early but outscored the Bucks 46-32 in the paint and outrebounded Milwaukee 48-38. The Grizzlies also went 6 of 10 beyond the arc.
The Bucks held a 13-point lead in the first half. Knight scored nine in the third, but Memphis began to make a push at the end of the period - even adding a point after it was over when officials reviewed a shot by Mike Miller and ruled it a 3. That left Milwaukee with a 69-67 lead entering the fourth.
Memphis finally erased the deficit early in the final quarter, opening with a 16-4 rally to build its first double-digit lead of the night.
Calathes sparked the burst with a trio of 3-pointers, the third one coming with 3:14 left for a 90-78 lead that Memphis never relinquished.
The Bucks controlled the first half as Memphis struggled to find its rhythm with Conley out. Milwaukee shot 43 percent and Ilyasova already was close to a double-double with 12 points and nine rebounds.
Meanwhile, Gasol had 11 points and Calathes scored 10 for Memphis, which shot 42 percent. Randolph and Tayshaun Prince were a combined 3 of 13 in the half, including Prince missing all four of his shots.
The Bucks built their lead to as many as 13 in the first half before taking a 49-43 lead into the break. Only a 3-pointer from Courtney Lee with a second left in the half got the Grizzlies that close.
NOTES: Conley missed two previous games this season with a bruised left thigh. ... Bucks C Zaza Pachulia returned after missing 28 games with a broken right foot. ... Memphis has a six-game winning streak over the Bucks.