Alexandrova is the highest-ranked player remaining in the tournament after top seed Bianca Andreescu withdrew on Tuesday with an abdominal injury.
The world number 33 converted six of her 10 break points to see off Burel 6-3, 6-4 in an hour and 10 minutes as she reached her fourth quarter-final of the season, two of those on clay.
Barbora Krejcikova awaits Alexandrova in the last eight after battling back from a set down to beat Caroline Garcia 3-6, 6-2, 6-1.
Previous Strasbourg champion Garcia held serve throughout the opening set to open up a convincing lead, but Krejcikova did likewise in the second and third sets to advance through.
Number four seed Yulia Putintseva is also into the quarter-finals after Jil Teichmann retired injured when two games down in the opening set.
Arantxa Rus had a walkover win of her own, with French wildcard Harmony Tan a set down when having to withdraw through injury.
Wednesday’s other matches also came to an early end because of rain.
Jule Niemeier leads Shelby Rogers 6-4, 2-1 ahead of the resumption of that match on Thursday, which is also when Zhang Shuai and Sorana Cirstea will begin their second-round contest – the winner of which will go through to the semis following Andreescu’s withdrawal
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