World number 34 Shapovalov will face Filip Krajinovic for the title after the Serb saw off Spanish fifth seed Pablo Carreno-Busta 4-6, 6-3, 6-3.
Murray, steadily rebuilding his game after career-saving hip surgery earlier this year, triumphed 3-6, 7-5, 6-2 in the semifinals.
Nadal, 33, met his wife through his younger sister Maribel, a childhood friend of Perello.
The 32-year-old British star, steadily rebuilding his career after major hip surgery earlier this year, defeated qualifier Copil.
The 18-year-old defeated Frances Tiafoe of the United States to make the last four of the European Open in Antwerp.
Three-time Grand Slam champion Murray is attempting to work his way back to form almost 10 months after career-saving hip surgery.
The 20-time Grand Slam champion returned to Roland Garros this year after a three year absence, falling to Rafael Nadal in the semifinals.
The teenager made headlines around the world on Sunday when she conquered her first career title in Linz, Austria.
Federer has won all four of the Grand Slam tournaments, as well as the ATP Tour Finals six times, but is still waiting to grab Olympic singles gold.
Now Daniil Medvedev is homing in on Roger Federer's third place in the world rankings before the year is out and chasing a first Grand Slam title next year.
Gauff will shoot up from 110 in the rankings into the 80s, according to WTA calculations, after becoming the youngest American to earn a WTA trophy since Jennifer Capriati at Toronto in 1991.
The 15-year-old is the youngest woman to make a WTA final since Nicole Vaidisova won the Tashkent title in 2004.
The US Open finalist defeated fellow rising star Stefanos Tsitsipas of Greece 7-6 (7/5), 7-5.
With Rafael Nadal absent from the tournament with a wrist injury, none of the vaunted "Big Three" will win the title on Sunday.
The 15-year-old became the youngest woman to reach a WTA semi-final since Nicole Vaidisova won the Tashkent title in 2004.