Tyreke Evans scored 14 of his 27 points in the fourth quarter for the Grizzlies, but Memphis couldn't hold off Milwaukee, which won its third straight.
Henson added six of his nine rebounds and one of his two blocked shots in the fourth quarter.
Khris Middleton also scored 17 points for the Bucks, who were paced by 27 points from Giannis Antetokounmpo -- his second-lowest total of the season -- and Eric Bledsoe finished with 15.
Dillion Brooks scored 19 points for Memphis, Marc Gasol added 16 and Mario Chalmers finished with 14 for the Grizzlies, who shot 48.7 percent from the floor and made 11 of 26 3-pointers.
Up 65-60 at halftime, the Grizzlies went flat in the third quarter, scoring just 12 points while hitting only 5 of 18 shots and going nearly five minutes without a point.
Evans closed the quarter with a layup with 1.3 seconds left, then scored the first seven points of the fourth, trying the score at 84 on a 3-pointer with 10:22 remaining.
Matthew Dellavedova stopped the run with a 3 of his own on the other end, but two free throws from Gasol and a 3 from Brooks made it 89-87 with 8:57 left.
The Grizzlies stretched the lead to five on a layup by Evans with 7:39 left before the Bucks recovered and tied the score at 96 on a 3-pointer from Tony Snell -- part of an 11-2 run that put the Bucks up 100-96 with 4:58 to play.
Henson scored six points in the final 3:08 and Memphis went 1 of 8 during that stretch, getting only a bucket from Brooks with 16 seconds remaining to pull the Grizzlies within five.
NOTES: Bucks G Eric Bledsoe made his third straight start despite suffering a bone bruise in Milwaukee's last outing. Coach Jason Kidd had said Bledsoe would be a "game-time decision." ... Memphis was without JaMychal Green (left ankle), but Jarell Martin, listed as questionable because of a sore right knee, was active and available against the Bucks. ... Tyreke Evans has scored at least 20 points off the bench in each of his last six games, extending his own franchise record. ... The Bucks have won three in a row, trying their longest winning streak of the season.