"Everybody knows when Dirk is out we have to step up a little bit and fill his void scoring the basketball," Williams said after his second-highest scoring game this season. "I was able to do that a little bit."
The Mavericks (28-22) went on a 21-3 run in the fourth quarter to pull away and finish off a three-game sweep of the season series with Phoenix.
The Suns fell to 14-35 after their fourth consecutive loss and 10th in their last 11 games. Phoenix, which is 2-19 since Dec. 20, led going into the fourth and held a 73-68 edge early in the final period.
"We don't have a lot of great scorers out there," Suns coach Jeff Hornecek said. "The guys that we have to score the ball need to score it. I don't know the last time we broke 100. Without Eric and Brandon there's not a lot of scoring."
The Mavericks continued their mastery over teams at the bottom of the standings, improving to 20-6 against teams with losing records.
Nowitzki, rested on the front end of a back-to-back, is expected back Monday night at Atlanta. Williams did his best Nowitzki impression by making 10 of 19 shots, including 2 of 5 3-pointers.
Williams also recovered from missing the morning shoot-around with an allergic reaction to suit up against the Suns.
"This is a team that's without a lot of their key guys due to injury, so we didn't want to come out and lay an egg," said Williams, whose season-high is 30 points against Portland on Dec. 1.
Mavericks small forward Chandler Parsons scored 15, with 12 coming in the first half. Point guard Raymond Felton, starting because of Nowitzki's absence, had 10 points and six assists. Center Zaza Pachulia grabbed 15 rebounds.
"We just had a lot of guys play big," Mavericks coach Rick Carlisle said. "Williams played a great game. I thought Felton down the stretch made great plays. Huge win with Dirk sitting out."
Rooking shooting guard Devin Booker paced the Suns with 19 points. Power forward Mirza Teletovic scored 14, but shot just 3 of 11. Center Tyson Chandler had 12 points and 13 boards.
Phoenix has lost 14 in a row on the road, tied for the second-longest such streak in franchise history.
"We have some guys hurt," Suns backup center Alex Len said. "We're a young group trying to learn, develop and get better from game to game."
Phoenix took a 65-60 lead in the third on a 10-0 run, with the last eight points coming Booker.
The Mavericks tied it at 65-65 after guard J.J. Barea scored five in a row, including a 3-pointer after Dallas had missed 10 straight from beyond the arc.
The Mavericks went into halftime up 51-45 by closing the second quarter with a 14-6 spurt. Williams had 18 points at the break.
Phoenix opens a season-long seven-game homestand Tuesday against Toronto.
NOTES: F Dirk Nowitzki sat out Sunday against the Suns in order to play Monday at Atlanta. "He's not playing back-to-backs right now," Mavericks coach Rick Carlisle said. ... Asked if the Mavericks are currently engaged in any trade talks, owner Mark Cuban said: "There's nothing really tempting us, no conversations." ... Dallas G Devin Harris (sprained toe) missed his fourth consecutive game due to a sprained toe. ... Phoenix PG Brandon Knight (groin strain) has missed his past six games. ... Suns F T.J. Warren was out with a right ankle impingement. ... The Suns and Mavericks met for the third and final time this season.