World number 15 Paul won his only prior ATP crown in 2021 at Stockholm but had lost in last year's finals at Acapulco and Eastbourne in his only other ATP championship matches.
Paul, who reached his first Grand Slam semi-final at last year's Australian Open, broke Giron for a 2-0 lead in the final set and held from there to take the victory on a service winner after two hours and 32 minutes.
Paul dominated the first-set tie-breaker but lost a battle for the second.
In a marathon ninth game that lasted more than 12 minutes, Paul held serve when Giron netted a forehand.
But Giron then held, broke for a 6-5 second-set edge when Paul sent a forehand long, then held again to force a third set.
Paul improved to 2-1 against Giron in ATP encounters, losing their inaugural meeting in a 2021 Miami Open first-round match but taking a round-of-16 affair last year in Canada.