A single break of serve in each set was enough to separate the two compatriots as Shelton emerged from the quarter-final battle a 6-4, 4-6, 6-3 winner.
The 24-year-old becomes the first American to reach the last four of the 1000-level event in the French capital since John Isner and eventual champion Jack Sock in 2017.
For world number 14 Paul, the defeat brought not only an end to his hunt for a first Masters title of his career, but also to his hopes of reaching this season's ATP Finals.
American Frances Tiafoe, who lost in the second round on Wednesday, is now assured of playing in the season-ender, which will run from November 15-22 in Turin.
On court, Paul was the first to crack when serving at 4-5 as two double faults presented Shelton with set points, the second of which the Atlanta native converted with a forehand winner.
But Paul hit back instantly, breaking Shelton to 15 in the very first game of the second frame.
With his nose ahead, the 29-year-old held firm to serve the match out to a decider.
The momentum swung back in Shelton's favour in the fourth game as the third seed converted a break point with an inside-out forehand that just nicked the outside of the line.
Shelton then kept Paul at arm's length to move into the next round, where he will meet either France's Luca Van Assche or Australian qualifier Rinky Hijikata.
Later, seven-time Grand Slam champion Carlos Alcaraz will take on Taylor Fritz for a spot in the semi-finals.
Former world number two Casper Ruud will close out the day's play against Portuguese lucky loser Nuno Borges.