Four-time Grand Slam champion Alcaraz brushed aside 84th-ranked German Altmaier 6-3, 6-1 to set up a last-eight clash with rising French star Arthur Fils on Friday.
Alcaraz took some time to find his rhythm as Altmaier broke him back to level at 3-3 in the first set, but it was one-way traffic from then on.
The second seed reeled off three straight games to take the first set before racing through the second in just over half an hour.
The 21-year-old, the reigning French Open and Wimbledon champion, is the favourite to lift the title this weekend after early exits for top seed Alexander Zverev and Novak Djokovic.
Alcaraz was beaten in his first match on his only previous appearance at the tournament in 2022.
Fils eased into his third successive Masters quarter-final this season with an impressive 6-2, 6-3 thrashing of 2023 champion Andrey Rublev.
The 20-year-old Fils is aiming to reach the semis of a Masters event for the first time, after losing in the last eight at both Indian Wells and the Miami Open this year.
