The 12th seed produced a composed performance to overcome the former Paris Masters champion, winning in one hour and 20 minutes on the indoor hard court.
Paul made the difference with his excellent serving and greater consistency, committing fewer unforced errors than Rune throughout the encounter.
The opening set was closely contested, with both players largely comfortable on serve. However, Paul eventually secured the crucial break after capitalising on a poor service game from the Dane.
Rune attempted to respond and showed resilience when facing pressure, saving three set points and creating opportunities to break back. Paul remained composed, however, using his powerful serve and timely aces to close out the set 7-5.
The American carried that momentum into the second set, breaking Rune's serve to establish a 2-1 advantage.
Paul continued to dictate the exchanges and secured another break to move 5-2 ahead, putting himself within touching distance of victory.
Rune refused to surrender without a fight. The 2022 Paris Masters champion saved a match point and broke back before holding serve to reduce the deficit to 5-4.
However, Paul maintained his composure in the next game, converting his second match point to seal a 7-5, 6-4 victory.
Paul keeps ATP Finals hopes alive
The victory is particularly important for Paul, who is attempting to secure qualification for the season-ending ATP Finals in Turin.
The American entered the tournament 13th in the Race to Turin and needs to reach at least the final in Paris to remain in contention, while winning the title would guarantee his qualification.
For Rune, the defeat ends his Paris Masters campaign following an encouraging return to competition after an 11-month absence caused by an Achilles tendon injury.
The 23-year-old Dane had reached the quarter-finals in Basel in his previous tournament, but Paul proved a tougher challenge.
Paul will now face Spain's Daniel Merida in the next round as he continues his pursuit of a place at the ATP Finals.