Steele won by one shot from South Africa's Louis Oosthuizen, finishing 18 under after firing a four-under 68 in Sunday's final round at the Grange Golf Club.
The 41-year-old Californian slept on a one-shot lead and says six-time major winner Mickelson was vital in calming his pre-round nerves.
"He was like 'how are you feeling, what are you thinking'," Steele said of his HyFlyers GC teammate.
"I said 'well, if I can play freely like I did the last couple days, I feel like I'll have a good chance'.
"He's like ... 'let's reframe it, let's make it "when" I play freely ... you will play freely, this is what you need to do'.
"Just for him to have that belief in me is really great, he is the reason that I'm here and the reason that I'm improving.
"To be honest, I'm 41 years old and I'm getting better and it's mostly because of him."
Steele shot a four-under 68 on Sunday and held off a charge from Oosthuizen (17 under), who carded a seven-under 65.
Louis Oosthuizen made a spirited charge during the final round of LIV Golf Adelaide. (Michael Errey/AAP PHOTOS)
Former world No.1 Jon Rahm (16 under) also threatened with an eagle and six birdies in a superb 64 but fell short.
Australia's Matt Jones (14 under) topped the standings for the locals, with Cameron Smith, Marc Leishman and Lucas Herbert all 13 under.
The Australian quartet claimed the teams title for their Ripper GC.
Individually, Smith started Sunday as the best-placed Australian at 11 under, three shots shy of overnight leader Steele.
But the Queenslander bogeyed the third hole, a 222-metre par-3, and watched a series of putts shave the hole in his two-under 70.
Compatriot Jones started the tournament with a six-under 66 and then four-under 68.
And the 44-year-old got hot in a seven-hole stretch that reaped his four birdies for the day.
Leishman carded a fine seven-under 65, while Herbert made a stunning comeback after a one-over 73 on the opening day.
Herbert shot a seven-under 65 on consecutive days to finish with a flourish.
Some notable big names were off the pace, including Brooks Koepka (nine under), Bryson DeChambeau (10 under), Dustin Johnson (nine under), Mickelson (seven under) and Sergio Garcia (six under).
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