The Suns pulled away in a rampant fourth-quarter run to win their second straight game against the defending NBA champions and send the best-of-seven series back to Los Angeles at 2-2.
"I believe that every night (I will shoot well). I put in the time and my team mates believe in me," Frye told reporters having sparked his team and a frenzied home crowd with three long-range shots in the second quarter.
"I have to thank team mates and coaches for believing in me. I take pride in wearing the Suns uniform."
Kobe Bryant sparkled with 38 points and 10 assists but his Lakers were left behind when the Suns sank three straight three-pointers to take control with an 98-89 lead in the fourth.
For the second straight contest, Phoenix used a zone defense to stifle Los Angeles, taking away their height advantage and forcing the visitors into long-distance shots.
However, the Suns bench can take most of the credit for the victory, outgunning the Lakers reserves by a massive 54-20 margin.
Reserve Leandro Barbosa chipped in with 14 of those points while Jared Dudley added 11.
Phoenix turned the game into a shootout by scoring 41 points in the second quarter on the way to establishing a nine-point lead at halftime.
The Lakers fought back behind the reliable hand of Bryant, who converted six three-pointers and tallied 16 in the third, and even led by two points with 10:48 remaining before the Suns caught fire from the outside.
"We didn't shut them down in the fourth and that's the time you have to do it," Lakers coach Phil Jackson said.
"The threes in the fourth were a real problem. We're disappointed. We thought we could come here and get a game but we weren't up to the task." (Reporting by Jahmal Corner in Los Angeles; Editing by John O'Brien)