It was the fourth straight win for Memphis, which led by 11 after one quarter and then repelled a brief second-half charge by the Trail Blazers.
Conley scored 20 points while Zach Randolph contributed 19 points and eight rebounds. The Grizzlies shot 51 percent from the field and held Portland to 4-of-29 from 3-point range.
Both J.J. Hickson and Damian Lillard had 17 points for Portland, which has lost six in a row.
This was the opener of a late-season, three-game road trip for the Grizzlies, who will also visit the Los Angeles Lakers and Sacramento before playing three of their final five games at home.
Celebrity Breakups and divorces of 2014 [PHOTOS]