Beal was unable to convert down the stretch, though, including missing a 21-footer with 12.9 seconds left that would have tied the game.
Zach Randolph split two free throws with 11.5 seconds left to give the Grizzlies the 92-89 lead. John Wall's 3-pointer with about 1 second left rattled around before popping out, giving Memphis the win.
Randolph, Courtney Lee and James Johnson scored 13 apiece for Memphis, and Randolph grabbed 10 rebounds. Calathes also had six assists for the Grizzlies.
Nene had 17 points for the Wizards, while Trevor Ariza and Marcin Gortat added 10 points each.
Memphis controlled the inside game, outrebounding the Wizards 40-33 and outscoring Washington in the paint 34-26.
Beal finished the night 15 of 24 from the field, including 5 of 7 from outside the arc. And, Beal was able to help keep Washington close, but struggled down the stretch, missing several key shots.
The Wizards, who trailed by as many as 16 in the third, were able to pull even at 80 with 6:52 left when Beal's 14-footer, pushed him past his previous career high of 34.
Beal was the major part of a 12-1 Wizards run to give them an 82-80 lead on Nene's 17-footer with 5:46 left. Memphis answered with a 7-2 mini-run to put the Grizzlies up for good, although each team made mistakes in the closing minutes.
Memphis outscored the Wizards 28-16 in the second quarter to carry a 52-39 lead into halftime. Gasol, Randolph and Johnson already had 10 apiece.
Beal was a major part of Washington's offense, shooting 8 of 10 from the field, including all three of his shots beyond the arc, for 19 points.
The rest of the Wizards were 8 of 27 from the field, resulting in Washington shooting 43 percent for the half. Memphis was at 53 percent.
Washington finished the game shooting 46 percent compared to 47 percent for Memphis.
The teams were tied at 28 with just under 8 minutes to play in the half when Memphis went on a 12-2 run to take a double-digit lead.
Memphis increased the lead to 16 near the 9-minute mark of the third quarter on a 3-pointer from Tayshaun Prince. But Washington, with Beal continuing to score and Gortat contributing 10 in the quarter, went on a 20-8 burst to make a serious dent in the Memphis margin.
By the end of the third, Memphis had added a few points to its lead carrying a 79-70 lead into the fourth.
NOTES: Memphis starting G Mike Conley missed his sixth straight game with a bum right ankle. The Grizzlies are now 3-3 since his injury. . Beal's previous high was 34 against Oklahoma City on Nov. 10. . Johnson recorded his 16th block of a 3-pointer this season near the end of the first half. . The Wizards have lost nine straight in Memphis and haven't won a road game in the series since Nov. 3, 2004, the night of the first regular-season game the Grizzlies played at FedExForum.