Rublev had already slammed his racquet to the ground during the opening game of the second set in Wednesday's round-robin match.
Then, when the Russian missed a shot to hand Alcaraz a break, he started beating himself as he walked to his chair and had to use a towel to wipe the blood off.
Blood continued to trickle down Rublev's leg as he played on and he eventually called a trainer for treatment.
"It's OK," Rublev shrugged afterwards. "I get disappointed and couldn't manage."
The second-ranked Alcaraz, a 20-year-old Spaniard who is already a two-time grand slam champion, ended an uncharacteristic three-match losing streak following defeats to Grigor Dimitrov in Shanghai, Roman Safiullin in Paris and Alexander Zverev in his debut match in Turin.
While Rublev was virtually eliminated after losing both of his opening matches, Alcaraz boosted his chances of advancing from the round robin stage at the season-ending event for the year's top eight players.
But the Spaniard will have to beat Daniil Medvedev, who was playing later in the red group on Wednesday against Zverev in an 18th meeting between the pair.
"The key against Medvedev is to play a perfect match — tactically," Alcaraz said.
Jannik Sinner leads the green group with two wins following his victory over Novak Djokovic on Tuesday, with the top two finishers in each four-man group advancing to the semi-finals.
The Alcaraz-Rublev match had proved a close affair in the opening set until the Spaniard broke for a 6-5 lead.
Then Rublev was left fuming as the opening point of the next game had to be replayed after his shot was called wide. The call was overturned on review after it was shown that the shot had landed on the line.
Rublev called it an "unlucky call."
"But it's part of the sport," he said. "It happens every match. ... Just happened that it was an important point."
In the next game, Rublev bloodied himself.
As the second set wore on, Alcaraz began producing one highlight after another. Like when he hit a forehand cross-court passing shot as he was in the process of falling down, and also when he pulled off a backhand winner down the line from far off court on the run a couple of games later.
