Alcaraz triumphed at the US Open on Monday (AEST), beating Casper Ruud to clinch his first grand slam title and, in the process, become the youngest world No.1 since the rankings were first published in 1973.
The 19-year-old is the second-youngest male player to win the title at Flushing Meadows in the Open Era, and only the third player since the Majors welcomed professionals in 1968 to win the US Open title at his first or second main draw appearance after Arthur Ashe and Rod Laver (in the first two editions of the tournament).
Yet back on home soil in Spain on Saturday (AEST), Alcaraz was unable to claim victory in his first match since becoming No.1, as he went down 6-7 (3-7) 6-4 6-2 to Auger-Aliassime in the Davis Cup Finals.
Canada's Auger-Aliassime did not concede a break point as he dragged his country level in its tie with Spain in Valencia, teeing up a doubles decider after Roberto Bautista Agut defeated Vasek Pospisil 3-6 6-3 6-3.
Auger-Aliassime, 22, has won both of his career matches against Alcaraz, after defeating him in the US Open quarter-finals last year.