Wimbledon champion Alcaraz toiled for three hours in stifling heat on Thursday to edge past fellow Spaniard Jaume Munar in a titanic scrap and afterwards admitted he did not know how he was still standing.
It was far more straightforward against unseeded Rinderknech, the player he also beat in his opening match two years ago when he went on to win the title at the prestigious Wimbledon warm-up event in west London.
The 22-year-old converted each of his two break points on another sweltering Friday as he extended his sequence of match wins to a career-long 16.
"I could be better. Honestly I was thinking I was going to feel much worse than I did today," five-time grand slam champion Alcaraz said on court.
"I'm glad it was only one hour 20 minutes today."
Britain's Jack Draper also continued his Wimbledon build-up successfully as he reached the semi-finals at Queen's for the first time with a 6-4 5-7 6-4 defeat of American Brandon Nakashima.
Draper not only kept himself on track for the prestigious ATP 500 title, but also secured the win that guarantees a top-four seeding at Wimbledon where he will be the big home hope.
The 23-year-old was fully tested by world No.32 Nakashima and his powerful game began to misfire as he lost the second set on the Andy Murray Arena.
But Draper settled back into the groove in the deciding set and broke serve in the seventh game with one of his trademark forehand pile drivers.
The left-hander had to save a break point when serving for the match at 5-4 but recovered to seal victory and set up a clash with Czech Jiri Lehecka, the conqueror of Alex de Minaur who had earlier on Friday beaten Britain's Jacob Fearnley 7-5 6-2.
"It means the world to me to reach the semi-finals here," said Draper, bidding to become the first British player to win the title at the prestigious west London club since Murray won for a record fifth time in 2016.
"I think there's going to be an even bigger buzz at the weekend and that will give me more energy to keep progressing."
While being ranked fourth means Draper will avoid either defending champion Alcaraz or world No.1 Jannik Sinner until the semi-finals at Wimbledon, Draper shrugged off its significance.
"I kept getting asked about that by the journalists but I've got to reach the semi-finals first," he said.
Alcaraz will face another Spaniard in the semi-final after Roberto Bautista Agut defeated fourth seed Holger Rune 7-6 (7-5) 6-7 (4-7) 6-2, the 37-year-old's first win over the Dane in four meetings.
Rune failed to force a single break point, but managed to save 12 of 14 himself to take Bautista Agut to a deciding set, where the Spaniard finally broke twice.
