In a clash between two unseeded players, Paul used his greater experience to grind down the 20-year-old 7-6 (8/6), 6-3, 5-7, 6-4 in a battle of attrition on Rod Laver Arena.
He will face either Serbian nine-time champion Novak Djokovic or Russian fifth seed Andrey Rublev for a place in Sunday's title match.
Paul is the first American man into the last four of the Australian Open since Andy Roddick in 2009.
Victory put the 25-year-old into his first major semi-final on the 14th attempt, with the world number 35's previous best at Wimbledon last year when he reached the fourth round.
Despite never playing a Slam quarter-final before, he had far more experience than Shelton, who was at only his second major and, remarkably, on his first trip overseas.
Paul leaned on that advantage and his returning prowess to disarm the left-hander's biggest weapons -- his serve and his forehand.
"Pumped to be here and obviously really excited for whoever I play next," said Paul, who has won one Tour-level title, on the Stockholm hardcourts in 2021, and achieved a career-high ranking of 28 last September.
"Making it to the second week of a Slam is everyone's dream when they play tennis. Can't believe I'm here right now.
"There wasn't too much rhythm in the match, but Ben is very tough to play against," he added.
"He's going to be in many, many more matches like this so everyone should be really excited for that kid."
In the biggest match of both players' careers, and their first against each other, the 89th-ranked Shelton opened with a decisive serve to love.
He saved a break point on his next service game, but the chances were limited in a tight baseline battle, with only the occasional foray to the net.
It went to a tiebreak where a netted backhand from Shelton gave Paul set point and the same shot handed him the set in 56 gruelling minutes.
Paul worked only the second break point of the match at 2-1 in the next set, but Shelton again clung on and then forced Paul to save two against him in the following game.
But as the pressure mounted, unforced errors began to creep in to Shelton's game and when he flayed a forehand wide from the baseline, Paul got the crucial break for a 4-2 lead and kept his composure to take the set with an ace.
Shelton fended off four break points at 1-1 in the third set as Paul went in for the kill, but his consistent countryman kept coming and finally forced the breakthrough for 4-3.
Undeterred, Shelton immediately got the set back on an even keel next game and stunned Paul with some power hitting to break again and take the match to a fourth set.
But the effort seemed to sap his energy and Paul romped to victory.