Memphis held a 20-point lead in the third quarter, but the Mavericks cut into the lead behind Wesley Matthews, who finished with 18 points and made four 3-pointers in the period.
A fourth-quarter push gave the Mavericks an 86-84 lead with 3:56 left when J.J. Barea converted three free throws, capping an 18-8 run to open the quarter.
That was the last lead for Dallas, as Conley scored the next five points and had nine of the Grizzlies' final 10.
Harrison Barnes led Dallas with 22 points. Dirk Nowitzki added 14.
The Grizzlies were seeking revenge on the second night of a back-to-back after losing 103-94 in Dallas on Wednesday.
Memphis built the lead to 64-44 in the third quarter, but the Mavericks answered with 21-6 run capped by a 3-pointer from Matthews to cut the advantage to 70-65 late in the third.
The Memphis advantage was 76-68 after three quarters.
Unlike Wednesday's loss, Memphis was the one that forced the tempo at the start. The Grizzlies were much more active on defense and got out on the break.
The lead would swell to 22 points in the first half, and despite a lull in the Memphis defensive effort, the Grizzlies carried a 54-35 lead into the break as Gasol scored 15 points.
Barnes had 12 points before the break to lead the Mavericks, who were stymied by shooting 27 percent, including missing 12 of 13 shots from outside the arc.
Dallas finished the night at 34 percent, but was 10 of 34 from 3-point range.
Mavericks: Nowitzki has scored 1,445 points against the Grizzlies, more than any active player. Only Kobe Bryant, with 1,636, has more points against the Grizzlies. . F Josh McRoberts (lower extremity injury), G Seth Curry (stress reaction left tibia) and Devin Harris (personal reasons) were not with team.
Grizzlies: Gasol has scored at least 25 points in every game this season, except the opener against New Orleans. . It was Gasol's fourth double-double of the season.
Mavericks: Host the Philadelphia 76ers on Saturday.
Grizzlies: Host the Houston Rockets on Saturday.
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