Rogers made 10-of-17 shots from the floor and drained 2-of-3 3-pointers, including one during a 15-0 third-quarter burst that gave Phoenix control.
The Suns trailed, 54-52, with 8:50 left in the quarter before Hardaway nailed a game-tying jumper and sank a pair of free throws to give them the lead for good with 7:46 remaining.
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from Jazz-Suns: 56k | 300k  Stephon Marbury attacks the basket against the Jazz. Barry Gossage NBAE/Getty Images |
"We came together," Rogers said. "We started off light, but we were able to turn it around and pull away from them and win the ballgame."
Marbury finished with eight points and 11 assists, and Marion had 16 points, seven rebounds and four blocks for Phoenix, which also has won three straight at home.
Phoenix shot 47 percent (41-of-86) and made 6-of-14 3-pointers. Dan Majerle made 3-of-7 shots from the arc, including a pair during a 10-2 run to close the third quarter after Utah had crept within 69-59.
Majerle finished with 11 points and five assists, and Outlaw added six points, six rebounds and matched a season high with five blocks.
The Suns have won three in a row overall for the first time this season are 6-2 since opening the campaign at 4-5.
"We look good, we feel good," Hardaway said. "We know it all starts with our defense and that's how we're trying to start every game off. We're going to go out and try to leave all the energy on the defensive end."
Karl Malone scored 15 points but was the only player in double figures for the Jazz.
"We can't always play a two-man game," Utah coach Jerry Sloan said. "You just have to have confidence in the people around you that they will make the play. I don't think we quit tonight."
Utah made just 4-of-20 shots in the third quarter and shot only 24 percent (9-of-38) after halftime.
"In the first half, we shot and passed the ball well," Sloan said. "Then, in the second half, we couldn't get up and down the floor because we took quick shots and let them do what they want."
The Jazz shot 57 percent (21-of-37) in the first 24 minutes, but managed just 29 points in the second half, a season-low for a Phoenix opponent.
"The guys rallied and played very, very well in the second half," Suns coach Scott Skiles said. "We were able to get the big lead because we always click offensively when we can stop people. They didn't get out on the break. Our people can get out on the break and we become a very exciting team."
Utah's Donyell Marshall had nine points and 11 rebounds before leaving with a strained groin in the third quarter. John Starks also scored nine off the bench and rookie Andrei Kirilenko added eight.
Utah has won just one of its last six road games and is off to its worst start (6-10) since the 1982-83 season.
"I am frustrated," Malone said. "We aren't even thinking about complete games right now. We are down quarter to quarter, but we just have to work our way out of it.
"In this league, it's easy to lose. Sometimes we play well and think there is light at the end of the tunnel. Then we play like we did tonight, and that is no consolation."