The Suns, who shot 60 percent, led by as many as 32 in the first half and 39 in the second to win consecutive games for the first time since Shaquille O'Neal joined the lineup 11 games ago.
"We're just scratching the surface of how good we can be," Stoudemire said.
Rudy Gay, who scored a career-best 36 when the teams met in Memphis on Feb. 26, led the Grizzlies with 20.
"They've definitely adjusted," Gay said of the Suns' improvement since that last meeting. "They're playing well with each other, and they're lethal when they do that."
Memphis, opening a three-game road trip, lost its 15th straight away from home and 17th in its last 19 overall.
On the heels of its 94-87 victory over San Antonio on Sunday, Phoenix climbed within a game of New Orleans for the No. 5 playoff spot in the tight Western Conference. New Orleans, however, owns the tiebreaker.
"You feed off each other and the team feels good about themselves right now," Phoenix coach Mike D'Antoni said. "Before, even when we had a big victory and came back and were flat, it was hard to understand sometimes. But there's some good stuff in the dressing room and some good stuff going on, and they're starting to believe it."
The Suns improved to 5-6 since O'Neal came to the team, with two of those victories against Memphis. O'Neal had two points and eight rebounds and six assists in 17 minutes. His only shot was a rebound basket with 7:45 to go in the third quarter.
"He didn't have a point the first half, but I thought he controlled the whole game," D'Antoni said.
Steve Nash cautioned that the Suns are far from a polished product, though.
"Yeah, we're growing," he said. "We have a lot of work to do. I don't think we should get too excited over it, but we are starting to see improvement. We are starting to see progress, and I think everyone's confidence is going to grow if we continue to grow like this."
The Suns had their running game going early and often, mounting a 25-5 run to go up 41-20 on Barbosa's three-point play on a fastbreak with 22.5 seconds to go in the first.
Hill and Stoudemire each scored 13 in the quarter. It only got worse for Memphis and first-year coach Marc Iavaroni, who was the top assistant to D'Antoni before taking the Grizzlies' job.
Iavaroni credited the Suns' effort but thought his team could have put up a better fight.
"We're going through some rebuilding times right now and our concentration is suffering because it's difficult with 20 games to go, 19 now, to really have something hard to play for," he said.
A 12-0 run put Phoenix ahead 64-32 on Nash's 12-footer with 4:13 left in the half. Phoenix ended the half with their 20th fastbreak point on a pass from Raja Bell to Barbosa for a layup with 4.1 seconds to go.
The Suns led 72-41 at the break. Phoenix had a 20-1 advantage in fastbreak points and 46-20 in points in the paint.
The lead twice reached 39 in the third quarter, at 98-59 and 100-61, the largest Suns lead and biggest Memphis deficit this season.
The biggest thrill of the night came when O'Neal went barreling toward the Suns bench in pursuit of a loose ball. The players and assistant coaches, remembering O'Neal's leap into the third row of seats against the Spurs, scattered like frightened pigeons.
"It was probably the highlight of the game," Hill said.
Memphis hasn't beaten Phoenix since Dec. 17, 2005. The Suns last lost at home to the Grizzlies a month earlier, on Nov. 16, 2005. ... Phoenix has two other active eight-game winning streaks against opponents -- against Toronto and Charlotte. ... O'Neal had assists on four of the Suns' first six baskets. ... The Suns are 2-1 with Golden State and Sacramento remaining on a five-game home stand.