Lucky loser O'Connell, who fell to compatriot John Millman in Monday's qualifying but still progressed to the Adelaide International 2 main draw, went toe-to-toe with the world No.35 in the 90-minute scrap.
But Paul pounced at the crucial moments, breaking O'Connell at 4-5 to claim the first set and repeating the dose at 5-6 after an equally evenly poised second set.
Paul's whipping serve was on song in his first match of the season, while a wicked cross-court, angled forehand secured the first set against the world No.79.
O'Connell showed his class with some clutch volleys and big forehands.
But Paul preyed on O'Connell's second serve and, after being denied on his first two match points, secured passage and a round-of-16 clash with Brit Jack Draper.
"Always tricky first match of the season, so I'm pretty happy with how I played," Paul said.
"We've had some wars (in previous matches), so I knew it would be tricky.
"Hopefully (after a good 2022 season) I keep going up, little by little."
O'Connell will switch focus to next week's Australian Open, the much-improved Sydney product now entrenched in the top 100 after surging about 400 places to sit just outside of the mark in 2019.
Albert Ramos-Vinolas will next face Millman, while Jason Kubler plays Tomas Martin Etcheverry on Tuesday night.
Defending champion and local favourite Thanasi Kokkinakis booked his spot in the second round with a 6-0 6-7 (5-7) 7-5 defeat of Alexei Popyrin on Monday night.
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