Dragic, who had just two points on 1-for-6 shooting through three quarters, was 5 for 6 in the fourth, including converting three three-point plays to help the Suns snap a two-game losing streak.
After the score was tied at 88, Dragic scored six straight points to put the game away.
Marcin Gortat led the Suns with 20 points on 8-for-10 shooting from the field, while Jermaine O'Neal had 14 points. Kendall Marshall added 11 points and Luis Scola finished with 10.
Jerryd Bayless scored a season-high 29 points on 11-for-15 shooting, including 3 of 4 on 3-pointers, to lead the Grizzlies. Zach Randolph had 21 points and 13 rebounds, and Tayshaun Prince scored 11 points.
Phoenix, which outscored Memphis 31-19 in the fourth, was able to hang on despite committing a season-high 22 turnovers, partly offset by shooting 51 percent. In addition to Gortat, O'Neal was 5 of 7 from the field, and Dragic finished 6 for 12.
The Suns outscored the Grizzlies 52-40 in the paint.
The start of the second half was full of poor shooting. The Suns started 1 of 8, and Memphis was 2 of 17 during one stretch
-- with many of those rebound tips that rolled off the rim.
The shooting percentages, which were so good in the first half, decreased to a more normal number.
Neither team was able to get much of a buffer, but Memphis did make a push behind Bayless late in the period, and a tip-in by Prince at the horn provided Memphis with a 71-65 lead entering the fourth.
That lead wouldn't hold up as Dragic converted consecutive three-point plays near the midpoint of the fourth, putting Phoenix up 80-79 with 5:50 remaining.
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Dragic converted another three-point play when he was fouled on a 10-footer in the lane for an 86-82 lead. Bayless, meanwhile, was still connecting from the top of the key, and despite Dragic's production, the Suns' lead never reached more than six.
The Suns opened the second quarter hitting their first three shots for a 12-2 run and the first double-digit lead of the game.
But Mike Conley's drive with 3 seconds remaining gave the Grizzlies a 52-50 lead at halftime.
Bayless had 14 points on 6-for-9 shooting in the opening half, while Randolph had 12 points on 7-for-8 shooting.
Gortat hit his first seven shots, part of Phoenix hitting 60 percent until the latter stages of the half. They ended the half at 53 percent, Gortat going 8 of 10 from the field.
He would not take a shot in the second half.
The Suns backcourt, featuring Dudley and Dragic, two of the Suns three leading scorers, were a combined 1 of 7 in the half for two points at halftime.
NOTES: Suns F Jermaine O'Neal returned to the lineup after missing the last seven games due to personal medical reasons. ... The officials reviewed a last-second tip-in by Prince at the end of the third before finally ruling that it came before the buzzer. The review was so close that all three officials looked at the shot on replay all the way through the break between the third and the fourth periods. ... Jared Dudley, who averages 12.2.points, third-best on the Suns, was scoreless in 17 minutes, missing all five of his shots. ... Bayless' previous season high was 23 at Oklahoma City on Jan. 31.
Press; By CLAY BAILEY]
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