The 28-year-old dropped just one game in the opening set but faced a far tougher challenge in the second as the Russian began to battle back.
Nevertheless, Alexandrova failed to capitalise on her six break point opportunities and ultimately lost 6-1 7-6 (4).
Muguruza will battle Russia's Daria Kasatkina for a place in the semi-finals. It took the 24-year-old just over an hour to seal progression as she powered past Elise Mertens 6-3 6-4.
Elsewhere, Tunisian player Ons Jabeur took out the former two-time Wimbledon champion, Petra Kvitova.
The 27-year-old sealed her place in the next round in straight sets, beating the Czech legend 6-4 6-4.
Next up for Jabeur is a clash with Anett Kontaveit. The Estonian breezed to the quarter-finals with a 6-3 6-1 victory over Romania's Elena-Gabriela Ruse.