Coming into this European clay-court swing, Draper had won nine of his 20 matches on the red dirt.
Now, having reached the Madrid final and caused problems for Alcaraz in Rome, he has emerged as a genuine force on the surface going into the French Open, which begins on 25 May.
This, though, was a reminder of what it takes to beat the world’s leading men’s clay-courter.
Building up his physical durability – having struggled with fitness issues in previous seasons – has been key to Draper’s improvement on a surface which does not come naturally to the left-hander.
All his greater physicality was needed against Alcaraz – a player who glides around the clay and has more time to employ his weapons effectively on the slower surface.
Draper pounced on a loose game to take a 4-2 lead in the first set, but he was unable to consolidate the break as Alcaraz returned superbly to instantly hit back.
Continuing to make Draper work hard behind the baseline in the points, and electing to employ the drop-shot more regularly to end them, helped Alcaraz switch momentum.
Draper began to look weary as Alcaraz won five straight games to move a set and a break up, but he demonstrated his improved durability by digging deep to find another wind.
Draper instantly broke back in the second set, breezing through his next few service games while ramping up the pressure on Alcaraz.
Suddenly, Alcaraz looked flustered as his serve came under intense scrutiny.
The Spaniard played more than twice as many service points as Draper across the opening eight games but hung on with the help of his forehand to keep the set on serve.
Not breaking serve ultimately knocked the stuffing out of Draper.
The British left-hander was broken to love in the ninth game, bowing his head at the changeover to signal his frustration, before Alcaraz confidently served out.
The victory moves the Spaniard above Zverev to second in the rankings – and, crucially, ensures he will be seeded second when he starts the defence of his Roland Garros crown.
